Merge branch 'feature/polynomials-sift' into feature/polynomials

kmath-core/src/commonMain/kotlin/space/kscience/kmath/operations/bufferOperation.kt

@@ -91,6 +91,15 @@ public inline fun <T : Any, R> Buffer<T>.fold(initial: R, operation: (acc: R, T)
     return accumulator
 }
 
+/**
+ * Fold given buffer according to indexed [operation]
+ */
+public inline fun <T : Any, R> Buffer<T>.foldIndexed(initial: R, operation: (index: Int, acc: R, T) -> R): R {
+    var accumulator = initial
+    for (index in this.indices) accumulator = operation(index, accumulator, get(index))
+    return accumulator
+}
+
 /**
  * Zip two buffers using given [transform].
  */

kmath-functions/src/commonMain/kotlin/space/kscience/kmath/functions/LabeledPolynomial.kt

@@ -7,26 +7,25 @@ package space.kscience.kmath.functions
 
 import space.kscience.kmath.expressions.Symbol
 import space.kscience.kmath.operations.Ring
-import space.kscience.kmath.operations.ScaleOperations
+import kotlin.jvm.JvmName
 import kotlin.math.max
 
 
 /**
- * Represents multivariate polynomials with labeled variables.
+ * Represents multivariate polynomial that stores its coefficients in a [Map] and terms' signatures in a [Map] that
+ * associates variables (of type [Symbol]) with their degree.
  *
- * @param C Ring in which the polynomial is considered.
+ * @param C the type of constants.
  */
 public data class LabeledPolynomial<C>
+@PublishedApi
 internal constructor(
     /**
-     * Map that collects coefficients of the polynomial. Every non-zero monomial
-     * `a x_1^{d_1} ... x_n^{d_n}` is represented as pair "key-value" in the map, where value is coefficients `a` and
-     * key is map that associates variables in the monomial with multiplicity of them occurring in the monomial.
-     * For example polynomial
-     * ```
-     * 5 a^2 c^3 - 6 b + 0 b c
-     * ```
-     * has coefficients represented as
+     * Map that contains coefficients of the polynomial.
+     *
+     * Every monomial `a x_1^{d_1} ... x_n^{d_n}` is stored as a pair "key-value" in the map, where the value is the
+     * coefficient `a` and the key is a map that associates variables in the monomial with their degree in the monomial.
+     * For example, coefficients of a polynomial `5 a^2 c^3 - 6 b` can be represented as
      * ```
      * mapOf(
      *      mapOf(
@@ -38,6 +37,22 @@ internal constructor(
      *      ) to (-6)
      * )
      * ```
+     * and also as
+     * ```
+     * mapOf(
+     *      mapOf(
+     *          a to 2,
+     *          c to 3
+     *      ) to 5,
+     *      mapOf(
+     *          b to 1
+     *      ) to (-6),
+     *      mapOf(
+     *          b to 1,
+     *          c to 1
+     *      ) to 0
+     * )
+     * ```
      * where `a`, `b` and `c` are corresponding [Symbol] objects.
      */
     public val coefficients: Map<Map<Symbol, UInt>, C>
@@ -46,69 +61,88 @@ internal constructor(
 }
 
 /**
- * Space of polynomials.
+ * Arithmetic context for multivariate polynomials with coefficients stored as a [Map] and terms' signatures stored as a
+ * [Map] constructed with the provided [ring] of constants.
  *
- * @param C the type of operated polynomials.
- * @param A the intersection of [Ring] of [C] and [ScaleOperations] of [C].
- * @param ring the [A] instance.
+ * @param C the type of constants. Polynomials have them a coefficients in their terms.
+ * @param A type of provided underlying ring of constants. It's [Ring] of [C].
+ * @param ring underlying ring of constants of type [A].
  */
 public class LabeledPolynomialSpace<C, A : Ring<C>>(
     public override val ring: A,
 ) : MultivariatePolynomialSpace<C, Symbol, LabeledPolynomial<C>>, PolynomialSpaceOverRing<C, LabeledPolynomial<C>, A> {
+    /**
+     * Returns sum of the variable represented as a monic monomial and the integer represented as a constant polynomial.
+     */
     public override operator fun Symbol.plus(other: Int): LabeledPolynomial<C> =
-        if (other == 0) LabeledPolynomial<C>(mapOf(
+        if (other == 0) LabeledPolynomialAsIs(mapOf(
             mapOf(this@plus to 1U) to constantOne,
         ))
-        else LabeledPolynomial<C>(mapOf(
+        else LabeledPolynomialAsIs(mapOf(
             mapOf(this@plus to 1U) to constantOne,
             emptyMap<Symbol, UInt>() to constantOne * other,
         ))
+    /**
+     * Returns difference between the variable represented as a monic monomial and the integer represented as a constant polynomial.
+     */
     public override operator fun Symbol.minus(other: Int): LabeledPolynomial<C> =
-        if (other == 0) LabeledPolynomial<C>(mapOf(
+        if (other == 0) LabeledPolynomialAsIs(mapOf(
             mapOf(this@minus to 1U) to -constantOne,
         ))
-        else LabeledPolynomial<C>(mapOf(
+        else LabeledPolynomialAsIs(mapOf(
             mapOf(this@minus to 1U) to -constantOne,
             emptyMap<Symbol, UInt>() to constantOne * other,
         ))
+    /**
+     * Returns product of the variable represented as a monic monomial and the integer represented as a constant polynomial.
+     */
     public override operator fun Symbol.times(other: Int): LabeledPolynomial<C> =
         if (other == 0) zero
-        else LabeledPolynomial<C>(mapOf(
+        else LabeledPolynomialAsIs(mapOf(
             mapOf(this to 1U) to constantOne * other,
         ))
 
+    /**
+     * Returns sum of the integer represented as a constant polynomial and the variable represented as a monic monomial.
+     */
     public override operator fun Int.plus(other: Symbol): LabeledPolynomial<C> =
-        if (this == 0) LabeledPolynomial<C>(mapOf(
+        if (this == 0) LabeledPolynomialAsIs(mapOf(
             mapOf(other to 1U) to constantOne,
         ))
-        else LabeledPolynomial<C>(mapOf(
+        else LabeledPolynomialAsIs(mapOf(
             mapOf(other to 1U) to constantOne,
             emptyMap<Symbol, UInt>() to constantOne * this@plus,
         ))
+    /**
+     * Returns difference between the integer represented as a constant polynomial and the variable represented as a monic monomial.
+     */
     public override operator fun Int.minus(other: Symbol): LabeledPolynomial<C> =
-        if (this == 0) LabeledPolynomial<C>(mapOf(
+        if (this == 0) LabeledPolynomialAsIs(mapOf(
             mapOf(other to 1U) to -constantOne,
         ))
-        else LabeledPolynomial<C>(mapOf(
+        else LabeledPolynomialAsIs(mapOf(
             mapOf(other to 1U) to -constantOne,
             emptyMap<Symbol, UInt>() to constantOne * this@minus,
         ))
+    /**
+     * Returns product of the integer represented as a constant polynomial and the variable represented as a monic monomial.
+     */
     public override operator fun Int.times(other: Symbol): LabeledPolynomial<C> =
         if (this == 0) zero
-        else LabeledPolynomial<C>(mapOf(
+        else LabeledPolynomialAsIs(mapOf(
             mapOf(other to 1U) to constantOne * this@times,
         ))
 
     /**
-     * Returns sum of the polynomial and the integer represented as polynomial.
+     * Returns sum of the polynomial and the integer represented as a polynomial.
      *
      * The operation is equivalent to adding [other] copies of unit polynomial to [this].
      */
     public override operator fun LabeledPolynomial<C>.plus(other: Int): LabeledPolynomial<C> =
         if (other == 0) this
         else with(coefficients) {
-            if (isEmpty()) LabeledPolynomial<C>(mapOf(emptyMap<Symbol, UInt>() to other.asConstant()))
-            else LabeledPolynomial<C>(
+            if (isEmpty()) LabeledPolynomialAsIs(mapOf(emptyMap<Symbol, UInt>() to other.asConstant()))
+            else LabeledPolynomialAsIs(
                 toMutableMap()
                     .apply {
                         val degs = emptyMap<Symbol, UInt>()
@@ -118,15 +152,15 @@ public class LabeledPolynomialSpace<C, A : Ring<C>>(
             )
         }
     /**
-     * Returns difference between the polynomial and the integer represented as polynomial.
+     * Returns difference between the polynomial and the integer represented as a polynomial.
      *
      * The operation is equivalent to subtraction [other] copies of unit polynomial from [this].
      */
     public override operator fun LabeledPolynomial<C>.minus(other: Int): LabeledPolynomial<C> =
         if (other == 0) this
         else with(coefficients) {
-            if (isEmpty()) LabeledPolynomial<C>(mapOf(emptyMap<Symbol, UInt>() to (-other).asConstant()))
-            else LabeledPolynomial<C>(
+            if (isEmpty()) LabeledPolynomialAsIs(mapOf(emptyMap<Symbol, UInt>() to (-other).asConstant()))
+            else LabeledPolynomialAsIs(
                 toMutableMap()
                     .apply {
                         val degs = emptyMap<Symbol, UInt>()
@@ -136,7 +170,7 @@ public class LabeledPolynomialSpace<C, A : Ring<C>>(
             )
         }
     /**
-     * Returns product of the polynomial and the integer represented as polynomial.
+     * Returns product of the polynomial and the integer represented as a polynomial.
      *
      * The operation is equivalent to sum of [other] copies of [this].
      */
@@ -151,15 +185,15 @@ public class LabeledPolynomialSpace<C, A : Ring<C>>(
         )
 
     /**
-     * Returns sum of the integer represented as polynomial and the polynomial.
+     * Returns sum of the integer represented as a polynomial and the polynomial.
      *
      * The operation is equivalent to adding [this] copies of unit polynomial to [other].
      */
     public override operator fun Int.plus(other: LabeledPolynomial<C>): LabeledPolynomial<C> =
         if (this == 0) other
         else with(other.coefficients) {
-            if (isEmpty()) LabeledPolynomial<C>(mapOf(emptyMap<Symbol, UInt>() to this@plus.asConstant()))
-            else LabeledPolynomial<C>(
+            if (isEmpty()) LabeledPolynomialAsIs(mapOf(emptyMap<Symbol, UInt>() to this@plus.asConstant()))
+            else LabeledPolynomialAsIs(
                 toMutableMap()
                     .apply {
                         val degs = emptyMap<Symbol, UInt>()
@@ -169,17 +203,19 @@ public class LabeledPolynomialSpace<C, A : Ring<C>>(
             )
         }
     /**
-     * Returns difference between the integer represented as polynomial and the polynomial.
+     * Returns difference between the integer represented as a polynomial and the polynomial.
      *
      * The operation is equivalent to subtraction [this] copies of unit polynomial from [other].
      */
     public override operator fun Int.minus(other: LabeledPolynomial<C>): LabeledPolynomial<C> =
         if (this == 0) other
         else with(other.coefficients) {
-            if (isEmpty()) LabeledPolynomial<C>(mapOf(emptyMap<Symbol, UInt>() to this@minus.asConstant()))
-            else LabeledPolynomial<C>(
+            if (isEmpty()) LabeledPolynomialAsIs(mapOf(emptyMap<Symbol, UInt>() to this@minus.asConstant()))
+            else LabeledPolynomialAsIs(
                 toMutableMap()
                     .apply {
+                        forEach { (key, value) -> if (key.isNotEmpty()) this[key] = -value }
+
                         val degs = emptyMap<Symbol, UInt>()
 
                         this[degs] = this@minus - getOrElse(degs) { constantZero }
@@ -187,7 +223,7 @@ public class LabeledPolynomialSpace<C, A : Ring<C>>(
             )
         }
     /**
-     * Returns product of the integer represented as polynomial and the polynomial.
+     * Returns product of the integer represented as a polynomial and the polynomial.
      *
      * The operation is equivalent to sum of [this] copies of [other].
      */
@@ -206,43 +242,61 @@ public class LabeledPolynomialSpace<C, A : Ring<C>>(
      */
     public override fun number(value: Int): LabeledPolynomial<C> = number(constantNumber(value))
 
-    public override operator fun C.plus(other: Symbol): LabeledPolynomial<C> =
-        LabeledPolynomial<C>(mapOf(
-            mapOf(other to 1U) to constantOne,
-            emptyMap<Symbol, UInt>() to this@plus,
-        ))
-    public override operator fun C.minus(other: Symbol): LabeledPolynomial<C> =
-        LabeledPolynomial<C>(mapOf(
-            mapOf(other to 1U) to -constantOne,
-            emptyMap<Symbol, UInt>() to this@minus,
-        ))
-    public override operator fun C.times(other: Symbol): LabeledPolynomial<C> =
-        LabeledPolynomial<C>(mapOf(
-            mapOf(other to 1U) to this@times,
-        ))
-
+    /**
+     * Returns sum of the variable represented as a monic monomial and the constant represented as a constant polynomial.
+     */
     public override operator fun Symbol.plus(other: C): LabeledPolynomial<C> =
-        LabeledPolynomial<C>(mapOf(
+        LabeledPolynomialAsIs(mapOf(
             mapOf(this@plus to 1U) to constantOne,
             emptyMap<Symbol, UInt>() to other,
         ))
+    /**
+     * Returns difference between the variable represented as a monic monomial and the constant represented as a constant polynomial.
+     */
     public override operator fun Symbol.minus(other: C): LabeledPolynomial<C> =
-        LabeledPolynomial<C>(mapOf(
+        LabeledPolynomialAsIs(mapOf(
             mapOf(this@minus to 1U) to -constantOne,
             emptyMap<Symbol, UInt>() to other,
         ))
+    /**
+     * Returns product of the variable represented as a monic monomial and the constant represented as a constant polynomial.
+     */
     public override operator fun Symbol.times(other: C): LabeledPolynomial<C> =
-        LabeledPolynomial<C>(mapOf(
+        LabeledPolynomialAsIs(mapOf(
             mapOf(this@times to 1U) to other,
         ))
 
     /**
-     * Returns sum of the constant represented as polynomial and the polynomial.
+     * Returns sum of the constant represented as a constant polynomial and the variable represented as a monic monomial.
+     */
+    public override operator fun C.plus(other: Symbol): LabeledPolynomial<C> =
+        LabeledPolynomialAsIs(mapOf(
+            mapOf(other to 1U) to constantOne,
+            emptyMap<Symbol, UInt>() to this@plus,
+        ))
+    /**
+     * Returns difference between the constant represented as a constant polynomial and the variable represented as a monic monomial.
+     */
+    public override operator fun C.minus(other: Symbol): LabeledPolynomial<C> =
+        LabeledPolynomialAsIs(mapOf(
+            mapOf(other to 1U) to -constantOne,
+            emptyMap<Symbol, UInt>() to this@minus,
+        ))
+    /**
+     * Returns product of the constant represented as a constant polynomial and the variable represented as a monic monomial.
+     */
+    public override operator fun C.times(other: Symbol): LabeledPolynomial<C> =
+        LabeledPolynomialAsIs(mapOf(
+            mapOf(other to 1U) to this@times,
+        ))
+
+    /**
+     * Returns sum of the constant represented as a polynomial and the polynomial.
      */
     override operator fun C.plus(other: LabeledPolynomial<C>): LabeledPolynomial<C> =
         with(other.coefficients) {
-            if (isEmpty()) LabeledPolynomial<C>(mapOf(emptyMap<Symbol, UInt>() to this@plus))
-            else LabeledPolynomial<C>(
+            if (isEmpty()) LabeledPolynomialAsIs(mapOf(emptyMap<Symbol, UInt>() to this@plus))
+            else LabeledPolynomialAsIs(
                 toMutableMap()
                     .apply {
                         val degs = emptyMap<Symbol, UInt>()
@@ -252,12 +306,12 @@ public class LabeledPolynomialSpace<C, A : Ring<C>>(
             )
         }
     /**
-     * Returns difference between the constant represented as polynomial and the polynomial.
+     * Returns difference between the constant represented as a polynomial and the polynomial.
      */
     override operator fun C.minus(other: LabeledPolynomial<C>): LabeledPolynomial<C> =
         with(other.coefficients) {
-            if (isEmpty()) LabeledPolynomial<C>(mapOf(emptyMap<Symbol, UInt>() to this@minus))
-            else LabeledPolynomial<C>(
+            if (isEmpty()) LabeledPolynomialAsIs(mapOf(emptyMap<Symbol, UInt>() to this@minus))
+            else LabeledPolynomialAsIs(
                 toMutableMap()
                     .apply {
                         forEach { (degs, c) -> if(degs.isNotEmpty()) this[degs] = -c }
@@ -269,10 +323,10 @@ public class LabeledPolynomialSpace<C, A : Ring<C>>(
             )
         }
     /**
-     * Returns product of the constant represented as polynomial and the polynomial.
+     * Returns product of the constant represented as a polynomial and the polynomial.
      */
     override operator fun C.times(other: LabeledPolynomial<C>): LabeledPolynomial<C> =
-        LabeledPolynomial<C>(
+        LabeledPolynomialAsIs(
             other.coefficients
                 .toMutableMap()
                 .apply {
@@ -281,12 +335,12 @@ public class LabeledPolynomialSpace<C, A : Ring<C>>(
         )
 
     /**
-     * Returns sum of the constant represented as polynomial and the polynomial.
+     * Returns sum of the constant represented as a polynomial and the polynomial.
      */
     override operator fun LabeledPolynomial<C>.plus(other: C): LabeledPolynomial<C> =
         with(coefficients) {
-            if (isEmpty()) LabeledPolynomial<C>(mapOf(emptyMap<Symbol, UInt>() to other))
-            else LabeledPolynomial<C>(
+            if (isEmpty()) LabeledPolynomialAsIs(mapOf(emptyMap<Symbol, UInt>() to other))
+            else LabeledPolynomialAsIs(
                 toMutableMap()
                     .apply {
                         val degs = emptyMap<Symbol, UInt>()
@@ -296,12 +350,12 @@ public class LabeledPolynomialSpace<C, A : Ring<C>>(
             )
         }
     /**
-     * Returns difference between the constant represented as polynomial and the polynomial.
+     * Returns difference between the constant represented as a polynomial and the polynomial.
      */
     override operator fun LabeledPolynomial<C>.minus(other: C): LabeledPolynomial<C> =
         with(coefficients) {
-            if (isEmpty()) LabeledPolynomial<C>(mapOf(emptyMap<Symbol, UInt>() to other))
-            else LabeledPolynomial<C>(
+            if (isEmpty()) LabeledPolynomialAsIs(mapOf(emptyMap<Symbol, UInt>() to other))
+            else LabeledPolynomialAsIs(
                 toMutableMap()
                     .apply {
                         forEach { (degs, c) -> if(degs.isNotEmpty()) this[degs] = -c }
@@ -313,10 +367,10 @@ public class LabeledPolynomialSpace<C, A : Ring<C>>(
             )
         }
     /**
-     * Returns product of the constant represented as polynomial and the polynomial.
+     * Returns product of the constant represented as a polynomial and the polynomial.
      */
     override operator fun LabeledPolynomial<C>.times(other: C): LabeledPolynomial<C> =
-        LabeledPolynomial<C>(
+        LabeledPolynomialAsIs(
             coefficients
                 .toMutableMap()
                 .apply {
@@ -330,40 +384,58 @@ public class LabeledPolynomialSpace<C, A : Ring<C>>(
     public override fun number(value: C): LabeledPolynomial<C> =
         LabeledPolynomial(mapOf(emptyMap<Symbol, UInt>() to value))
 
+    /**
+     * Represents the variable as a monic monomial.
+     */
     public override operator fun Symbol.unaryPlus(): LabeledPolynomial<C> =
-        LabeledPolynomial<C>(mapOf(
+        LabeledPolynomialAsIs(mapOf(
             mapOf(this to 1U) to constantOne,
         ))
+    /**
+     * Returns negation of representation of the variable as a monic monomial.
+     */
     public override operator fun Symbol.unaryMinus(): LabeledPolynomial<C> =
-        LabeledPolynomial<C>(mapOf(
+        LabeledPolynomialAsIs(mapOf(
             mapOf(this to 1U) to -constantOne,
         ))
+    /**
+     * Returns sum of the variables represented as monic monomials.
+     */
     public override operator fun Symbol.plus(other: Symbol): LabeledPolynomial<C> =
-        if (this == other) LabeledPolynomial<C>(mapOf(
+        if (this == other) LabeledPolynomialAsIs(mapOf(
             mapOf(this to 1U) to constantOne * 2
         ))
-        else LabeledPolynomial<C>(mapOf(
+        else LabeledPolynomialAsIs(mapOf(
             mapOf(this to 1U) to constantOne,
             mapOf(other to 1U) to constantOne,
         ))
+    /**
+     * Returns difference between the variables represented as monic monomials.
+     */
     public override operator fun Symbol.minus(other: Symbol): LabeledPolynomial<C> =
         if (this == other) zero
-        else LabeledPolynomial<C>(mapOf(
+        else LabeledPolynomialAsIs(mapOf(
             mapOf(this to 1U) to constantOne,
             mapOf(other to 1U) to -constantOne,
         ))
+    /**
+     * Returns product of the variables represented as monic monomials.
+     */
     public override operator fun Symbol.times(other: Symbol): LabeledPolynomial<C> =
-        if (this == other) LabeledPolynomial<C>(mapOf(
+        if (this == other) LabeledPolynomialAsIs(mapOf(
             mapOf(this to 2U) to constantOne
         ))
-        else LabeledPolynomial<C>(mapOf(
+        else LabeledPolynomialAsIs(mapOf(
             mapOf(this to 1U, other to 1U) to constantOne,
         ))
 
+    /**
+     * Returns sum of the variable represented as a monic monomial and the polynomial.
+     */
     public override operator fun Symbol.plus(other: LabeledPolynomial<C>): LabeledPolynomial<C> =
         with(other.coefficients) {
-            if (isEmpty()) LabeledPolynomial<C>(mapOf(mapOf(this@plus to 1u) to constantOne))
-            else LabeledPolynomial<C>(
+            if (isEmpty()) LabeledPolynomialAsIs(mapOf(mapOf(this@plus to 1u) to constantOne))
+            else LabeledPolynomialAsIs(
                 toMutableMap()
                     .apply {
                         val degs = mapOf(this@plus to 1U)
@@ -372,30 +444,39 @@ public class LabeledPolynomialSpace<C, A : Ring<C>>(
                     }
             )
         }
+    /**
+     * Returns difference between the variable represented as a monic monomial and the polynomial.
+     */
     public override operator fun Symbol.minus(other: LabeledPolynomial<C>): LabeledPolynomial<C> =
         with(other.coefficients) {
-            if (isEmpty()) LabeledPolynomial<C>(mapOf(mapOf(this@minus to 1u) to constantOne))
-            else LabeledPolynomial<C>(
+            if (isEmpty()) LabeledPolynomialAsIs(mapOf(mapOf(this@minus to 1u) to constantOne))
+            else LabeledPolynomialAsIs(
                 toMutableMap()
                     .apply {
-                        forEach { (degs, c) -> if(degs.isNotEmpty()) this[degs] = -c }
-
                         val degs = mapOf(this@minus to 1U)
 
+                        forEach { (degs, c) -> if(degs != degs) this[degs] = -c }
+
                         this[degs] = constantOne - getOrElse(degs) { constantZero }
                     }
             )
         }
+    /**
+     * Returns product of the variable represented as a monic monomial and the polynomial.
+     */
     public override operator fun Symbol.times(other: LabeledPolynomial<C>): LabeledPolynomial<C> =
-        LabeledPolynomial<C>(
+        LabeledPolynomialAsIs(
             other.coefficients
                 .mapKeys { (degs, _) -> degs.toMutableMap().also{ it[this] = if (this in it) it[this]!! + 1U else 1U } }
         )
 
+    /**
+     * Returns sum of the polynomial and the variable represented as a monic monomial.
+     */
     public override operator fun LabeledPolynomial<C>.plus(other: Symbol): LabeledPolynomial<C> =
         with(coefficients) {
-            if (isEmpty()) LabeledPolynomial<C>(mapOf(mapOf(other to 1u) to constantOne))
-            else LabeledPolynomial<C>(
+            if (isEmpty()) LabeledPolynomialAsIs(mapOf(mapOf(other to 1u) to constantOne))
+            else LabeledPolynomialAsIs(
                 toMutableMap()
                     .apply {
                         val degs = mapOf(other to 1U)
@@ -404,10 +485,13 @@ public class LabeledPolynomialSpace<C, A : Ring<C>>(
                     }
             )
         }
+    /**
+     * Returns difference between the polynomial and the variable represented as a monic monomial.
+     */
     public override operator fun LabeledPolynomial<C>.minus(other: Symbol): LabeledPolynomial<C> =
         with(coefficients) {
-            if (isEmpty()) LabeledPolynomial<C>(mapOf(mapOf(other to 1u) to constantOne))
-            else LabeledPolynomial<C>(
+            if (isEmpty()) LabeledPolynomialAsIs(mapOf(mapOf(other to 1u) to constantOne))
+            else LabeledPolynomialAsIs(
                 toMutableMap()
                     .apply {
                         val degs = mapOf(other to 1U)
@@ -416,8 +500,11 @@ public class LabeledPolynomialSpace<C, A : Ring<C>>(
                     }
             )
         }
+    /**
+     * Returns product of the polynomial and the variable represented as a monic monomial.
+     */
     public override operator fun LabeledPolynomial<C>.times(other: Symbol): LabeledPolynomial<C> =
-        LabeledPolynomial<C>(
+        LabeledPolynomialAsIs(
             coefficients
                 .mapKeys { (degs, _) -> degs.toMutableMap().also{ it[other] = if (other in it) it[other]!! + 1U else 1U } }
         )
@@ -426,14 +513,14 @@ public class LabeledPolynomialSpace<C, A : Ring<C>>(
      * Returns negation of the polynomial.
      */
     override fun LabeledPolynomial<C>.unaryMinus(): LabeledPolynomial<C> =
-        LabeledPolynomial<C>(
+        LabeledPolynomialAsIs(
             coefficients.mapValues { -it.value }
         )
     /**
      * Returns sum of the polynomials.
      */
     override operator fun LabeledPolynomial<C>.plus(other: LabeledPolynomial<C>): LabeledPolynomial<C> =
-        LabeledPolynomial<C>(
+        LabeledPolynomialAsIs(
             buildMap(coefficients.size + other.coefficients.size) {
                 other.coefficients.mapValuesTo(this) { it.value }
                 other.coefficients.mapValuesTo(this) { (key, value) -> if (key in this) this[key]!! + value else value }
@@ -443,7 +530,7 @@ public class LabeledPolynomialSpace<C, A : Ring<C>>(
      * Returns difference of the polynomials.
      */
     override operator fun LabeledPolynomial<C>.minus(other: LabeledPolynomial<C>): LabeledPolynomial<C> =
-        LabeledPolynomial<C>(
+        LabeledPolynomialAsIs(
             buildMap(coefficients.size + other.coefficients.size) {
                 other.coefficients.mapValuesTo(this) { it.value }
                 other.coefficients.mapValuesTo(this) { (key, value) -> if (key in this) this[key]!! - value else -value }
@@ -453,7 +540,7 @@ public class LabeledPolynomialSpace<C, A : Ring<C>>(
      * Returns product of the polynomials.
      */
     override operator fun LabeledPolynomial<C>.times(other: LabeledPolynomial<C>): LabeledPolynomial<C> =
-        LabeledPolynomial<C>(
+        LabeledPolynomialAsIs(
             buildMap(coefficients.size * other.coefficients.size) {
                 for ((degs1, c1) in coefficients) for ((degs2, c2) in other.coefficients) {
                     val degs = degs1.toMutableMap()
@@ -467,18 +554,18 @@ public class LabeledPolynomialSpace<C, A : Ring<C>>(
     /**
      * Instance of zero polynomial (zero of the polynomial ring).
      */
-    override val zero: LabeledPolynomial<C> = LabeledPolynomial<C>(mapOf(emptyMap<Symbol, UInt>() to constantZero))
+    override val zero: LabeledPolynomial<C> = LabeledPolynomialAsIs(mapOf(emptyMap<Symbol, UInt>() to constantZero))
     /**
      * Instance of unit polynomial (unit of the polynomial ring).
      */
-    override val one: LabeledPolynomial<C> = LabeledPolynomial<C>(mapOf(emptyMap<Symbol, UInt>() to constantOne))
+    override val one: LabeledPolynomial<C> = LabeledPolynomialAsIs(mapOf(emptyMap<Symbol, UInt>() to constantOne))
 
     /**
      * Degree of the polynomial, [see also](https://en.wikipedia.org/wiki/Degree_of_a_polynomial). If the polynomial is
      * zero, degree is -1.
      */
     override val LabeledPolynomial<C>.degree: Int
-        get() = coefficients.entries.maxOfOrNull { (degs, c) -> degs.values.sum().toInt() } ?: -1
+        get() = coefficients.entries.maxOfOrNull { (degs, _) -> degs.values.sum().toInt() } ?: -1
     /**
      * Map that associates variables (that appear in the polynomial in positive exponents) with their most exponents
      * in which they are appeared in the polynomial.
@@ -518,22 +605,17 @@ public class LabeledPolynomialSpace<C, A : Ring<C>>(
      */
     public override val LabeledPolynomial<C>.countOfVariables: Int get() = variables.size
 
-//    @Suppress("NOTHING_TO_INLINE")
-//    public inline fun LabeledPolynomial<C>.substitute(argument: Map<Symbol, C>): LabeledPolynomial<C> = this.substitute(ring, argument)
-//    @Suppress("NOTHING_TO_INLINE")
-//    @JvmName("substitutePolynomial")
-//    public inline fun LabeledPolynomial<C>.substitute(argument: Map<Symbol, LabeledPolynomial<C>>): LabeledPolynomial<C> = this.substitute(ring, argument)
-//
-//    @Suppress("NOTHING_TO_INLINE")
-//    public inline fun LabeledPolynomial<C>.asFunction(): (Map<Symbol, C>) -> LabeledPolynomial<C> = { this.substitute(ring, it) }
-//    @Suppress("NOTHING_TO_INLINE")
-//    public inline fun LabeledPolynomial<C>.asFunctionOnConstants(): (Map<Symbol, C>) -> LabeledPolynomial<C> = { this.substitute(ring, it) }
-//    @Suppress("NOTHING_TO_INLINE")
-//    public inline fun LabeledPolynomial<C>.asFunctionOnPolynomials(): (Map<Symbol, LabeledPolynomial<C>>) -> LabeledPolynomial<C> = { this.substitute(ring, it) }
-//
-//    @Suppress("NOTHING_TO_INLINE")
-//    public inline operator fun LabeledPolynomial<C>.invoke(argument: Map<Symbol, C>): LabeledPolynomial<C> = this.substitute(ring, argument)
-//    @Suppress("NOTHING_TO_INLINE")
-//    @JvmName("invokePolynomial")
-//    public inline operator fun LabeledPolynomial<C>.invoke(argument: Map<Symbol, LabeledPolynomial<C>>): LabeledPolynomial<C> = this.substitute(ring, argument)
+    // TODO: When context receivers will be ready move all of this substitutions and invocations to utilities with
+    //  [ListPolynomialSpace] as a context receiver
+    /**
+     * Substitutes provided arguments [arguments] into [this] polynomial.
+     */
+    @Suppress("NOTHING_TO_INLINE")
+    public inline fun LabeledPolynomial<C>.substitute(arguments: Map<Symbol, C>): LabeledPolynomial<C> = substitute(ring, arguments)
+    /**
+     * Substitutes provided arguments [arguments] into [this] polynomial.
+     */
+    @Suppress("NOTHING_TO_INLINE")
+    @JvmName("substitutePolynomial")
+    public inline fun LabeledPolynomial<C>.substitute(arguments: Map<Symbol, LabeledPolynomial<C>>) : LabeledPolynomial<C> = substitute(ring, arguments)
 }

kmath-functions/src/commonMain/kotlin/space/kscience/kmath/functions/LabeledRationalFunction.kt

@@ -7,9 +7,12 @@ package space.kscience.kmath.functions
 
 import space.kscience.kmath.expressions.Symbol
 import space.kscience.kmath.operations.Ring
-import space.kscience.kmath.operations.invoke
+import kotlin.jvm.JvmName
 
 
+/**
+ * Represents multivariate rational function that stores its numerator and denominator as [LabeledPolynomial]s.
+ */
 public class LabeledRationalFunction<C>(
     public override val numerator: LabeledPolynomial<C>,
     public override val denominator: LabeledPolynomial<C>
@@ -17,6 +20,13 @@ public class LabeledRationalFunction<C>(
     override fun toString(): String = "LabeledRationalFunction${numerator.coefficients}/${denominator.coefficients}"
 }
 
+/**
+ * Arithmetic context for univariate rational functions with numerator and denominator represented as [LabeledPolynomial]s.
+ *
+ * @param C the type of constants. Polynomials have them a coefficients in their terms.
+ * @param A type of provided underlying ring of constants. It's [Ring] of [C].
+ * @param ring underlying ring of constants of type [A].
+ */
 public class LabeledRationalFunctionSpace<C, A: Ring<C>>(
     public val ring: A,
 ) :
@@ -34,106 +44,53 @@ public class LabeledRationalFunctionSpace<C, A: Ring<C>>(
             LabeledRationalFunction<C>,
             >() {
 
+    /**
+     * Underlying polynomial ring. Its polynomial operations are inherited by local polynomial operations.
+     */
     override val polynomialRing : LabeledPolynomialSpace<C, A> = LabeledPolynomialSpace(ring)
+    /**
+     * Constructor of rational functions (of type [LabeledRationalFunction]) from numerator and denominator (of type [LabeledPolynomial]).
+     */
     override fun constructRationalFunction(
         numerator: LabeledPolynomial<C>,
         denominator: LabeledPolynomial<C>
     ): LabeledRationalFunction<C> =
         LabeledRationalFunction<C>(numerator, denominator)
 
+    // TODO: When context receivers will be ready move all of this substitutions and invocations to utilities with
+    //  [ListPolynomialSpace] as a context receiver
     /**
-     * Instance of zero rational function (zero of the rational functions ring).
+     * Substitutes provided constant [argument] into [this] polynomial.
      */
-    public override val zero: LabeledRationalFunction<C> = LabeledRationalFunction<C>(polynomialZero, polynomialOne)
+    @Suppress("NOTHING_TO_INLINE")
+    public inline fun LabeledPolynomial<C>.substitute(argument: Map<Symbol, C>): LabeledPolynomial<C> = substitute(ring, argument)
     /**
-     * Instance of unit polynomial (unit of the rational functions ring).
+     * Substitutes provided polynomial [argument] into [this] polynomial.
      */
-    public override val one: LabeledRationalFunction<C> = LabeledRationalFunction<C>(polynomialOne, polynomialOne)
-
-    // TODO: Разобрать
-
-//    operator fun invoke(arg: Map<Symbol, C>): LabeledRationalFunction<C> =
-//        LabeledRationalFunction(
-//            numerator(arg),
-//            denominator(arg)
-//        )
-//
-//    @JvmName("invokeLabeledPolynomial")
-//    operator fun invoke(arg: Map<Symbol, LabeledPolynomial<C>>): LabeledRationalFunction<C> =
-//        LabeledRationalFunction(
-//            numerator(arg),
-//            denominator(arg)
-//        )
-//
-//    @JvmName("invokeLabeledRationalFunction")
-//    operator fun invoke(arg: Map<Symbol, LabeledRationalFunction<C>>): LabeledRationalFunction<C> {
-//        var num = numerator invokeRFTakeNumerator arg
-//        var den = denominator invokeRFTakeNumerator arg
-//        for (variable in variables) if (variable in arg) {
-//            val degreeDif = degrees[variable]!!
-//            if (degreeDif > 0)
-//                den = multiplyByPower(den, arg[variable]!!.denominator, degreeDif)
-//            else
-//                num = multiplyByPower(num, arg[variable]!!.denominator, -degreeDif)
-//        }
-//        return LabeledRationalFunction(num, den)
-//    }
-//
-//    override fun toString(): String = toString(emptyMap())
-//
-//    fun toString(names: Map<Symbol, String> = emptyMap()): String =
-//        when (true) {
-//            numerator.isZero() -> "0"
-//            denominator.isOne() -> numerator.toString(names)
-//            else -> "${numerator.toStringWithBrackets(names)}/${denominator.toStringWithBrackets(names)}"
-//        }
-//
-//    fun toString(namer: (Symbol) -> String): String =
-//        when (true) {
-//            numerator.isZero() -> "0"
-//            denominator.isOne() -> numerator.toString(namer)
-//            else -> "${numerator.toStringWithBrackets(namer)}/${denominator.toStringWithBrackets(namer)}"
-//        }
-//
-//    fun toStringWithBrackets(names: Map<Symbol, String> = emptyMap()): String =
-//        when (true) {
-//            numerator.isZero() -> "0"
-//            denominator.isOne() -> numerator.toStringWithBrackets(names)
-//            else -> "(${numerator.toStringWithBrackets(names)}/${denominator.toStringWithBrackets(names)})"
-//        }
-//
-//    fun toStringWithBrackets(namer: (Symbol) -> String): String =
-//        when (true) {
-//            numerator.isZero() -> "0"
-//            denominator.isOne() -> numerator.toStringWithBrackets(namer)
-//            else -> "(${numerator.toStringWithBrackets(namer)}/${denominator.toStringWithBrackets(namer)})"
-//        }
-//
-//    fun toReversedString(names: Map<Symbol, String> = emptyMap()): String =
-//        when (true) {
-//            numerator.isZero() -> "0"
-//            denominator.isOne() -> numerator.toReversedString(names)
-//            else -> "${numerator.toReversedStringWithBrackets(names)}/${denominator.toReversedStringWithBrackets(names)}"
-//        }
-//
-//    fun toReversedString(namer: (Symbol) -> String): String =
-//        when (true) {
-//            numerator.isZero() -> "0"
-//            denominator.isOne() -> numerator.toReversedString(namer)
-//            else -> "${numerator.toReversedStringWithBrackets(namer)}/${denominator.toReversedStringWithBrackets(namer)}"
-//        }
-//
-//    fun toReversedStringWithBrackets(names: Map<Symbol, String> = emptyMap()): String =
-//        when (true) {
-//            numerator.isZero() -> "0"
-//            denominator.isOne() -> numerator.toReversedStringWithBrackets(names)
-//            else -> "(${numerator.toReversedStringWithBrackets(names)}/${denominator.toReversedStringWithBrackets(names)})"
-//        }
-//
-//    fun toReversedStringWithBrackets(namer: (Symbol) -> String): String =
-//        when (true) {
-//            numerator.isZero() -> "0"
-//            denominator.isOne() -> numerator.toReversedStringWithBrackets(namer)
-//            else -> "(${numerator.toReversedStringWithBrackets(namer)}/${denominator.toReversedStringWithBrackets(namer)})"
-//        }
+    @Suppress("NOTHING_TO_INLINE")
+    @JvmName("substitutePolynomial")
+    public inline fun LabeledPolynomial<C>.substitute(argument: Map<Symbol, LabeledPolynomial<C>>): LabeledPolynomial<C> = substitute(ring, argument)
+    /**
+     * Substitutes provided rational function [argument] into [this] polynomial.
+     */
+    @Suppress("NOTHING_TO_INLINE")
+    @JvmName("substituteRationalFunction")
+    public inline fun LabeledPolynomial<C>.substitute(argument: Map<Symbol, LabeledRationalFunction<C>>): LabeledRationalFunction<C> = substitute(ring, argument)
+    /**
+     * Substitutes provided constant [argument] into [this] rational function.
+     */
+    @Suppress("NOTHING_TO_INLINE")
+    public inline fun LabeledRationalFunction<C>.substitute(argument: Map<Symbol, C>): LabeledRationalFunction<C> = substitute(ring, argument)
+    /**
+     * Substitutes provided polynomial [argument] into [this] rational function.
+     */
+    @Suppress("NOTHING_TO_INLINE")
+    @JvmName("substitutePolynomial")
+    public inline fun LabeledRationalFunction<C>.substitute(argument: Map<Symbol, LabeledPolynomial<C>>): LabeledRationalFunction<C> = substitute(ring, argument)
+    /**
+     * Substitutes provided rational function [argument] into [this] rational function.
+     */
+    @Suppress("NOTHING_TO_INLINE")
+    @JvmName("substituteRationalFunction")
+    public inline fun LabeledRationalFunction<C>.substitute(argument: Map<Symbol, LabeledRationalFunction<C>>): LabeledRationalFunction<C> = substitute(ring, argument)
 }

kmath-functions/src/commonMain/kotlin/space/kscience/kmath/functions/ListPolynomial.kt

@@ -8,23 +8,19 @@ package space.kscience.kmath.functions
 import space.kscience.kmath.operations.Ring
 import space.kscience.kmath.operations.ScaleOperations
 import space.kscience.kmath.operations.invoke
-import kotlin.contracts.InvocationKind
-import kotlin.contracts.contract
-import kotlin.experimental.ExperimentalTypeInference
-import kotlin.jvm.JvmName
 import kotlin.math.max
 import kotlin.math.min
 
 
 /**
- * Polynomial model without fixation on specific context they are applied to.
+ * Represents univariate polynomial that stores its coefficients in a [List].
  *
- * @param coefficients constant is the leftmost coefficient.
+ * @param C the type of constants.
  */
 public data class ListPolynomial<C>(
     /**
-     * List that collects coefficients of the polynomial. Every monomial `a x^d` is represented as a coefficients
-     * `a` placed into the list with index `d`. For example coefficients of polynomial `5 x^2 - 6` can be represented as
+     * List that contains coefficients of the polynomial. Every monomial `a x^d` is stored as a coefficient `a` placed
+     * into the list at index `d`. For example, coefficients of a polynomial `5 x^2 - 6` can be represented as
      * ```
      * listOf(
      *     -6, // -6 +
@@ -42,26 +38,28 @@ public data class ListPolynomial<C>(
      *     0,  // 0 x^4
      * )
      * ```
-     * It is recommended not to put extra zeros at end of the list (as for `0x^3` and `0x^4` in the example), but is not
-     * prohibited.
+     * It is not prohibited to put extra zeros at end of the list (as for `0x^3` and `0x^4` in the example). But the
+     * longer the coefficients list the worse performance of arithmetical operations performed on it. Thus, it is
+     * recommended not to put (or even to remove) extra (or useless) coefficients at the end of the coefficients list.
      */
     public val coefficients: List<C>
 ) : Polynomial<C> {
-    override fun toString(): String = "Polynomial$coefficients"
+    override fun toString(): String = "ListPolynomial$coefficients"
 }
 
 /**
- * Space of univariate polynomials constructed over ring.
+ * Arithmetic context for univariate polynomials with coefficients stored as a [List] constructed with the provided
+ * [ring] of constants.
  *
- * @param C the type of constants. Polynomials have them as a coefficients in their terms.
- * @param A type of underlying ring of constants. It's [Ring] of [C].
+ * @param C the type of constants. Polynomials have them a coefficients in their terms.
+ * @param A type of provided underlying ring of constants. It's [Ring] of [C].
  * @param ring underlying ring of constants of type [A].
  */
 public open class ListPolynomialSpace<C, A : Ring<C>>(
     public override val ring: A,
 ) : PolynomialSpaceOverRing<C, ListPolynomial<C>, A> {
     /**
-     * Returns sum of the polynomial and the integer represented as polynomial.
+     * Returns sum of the polynomial and the integer represented as a polynomial.
      *
      * The operation is equivalent to adding [other] copies of unit polynomial to [this].
      */
@@ -79,7 +77,7 @@ public open class ListPolynomialSpace<C, A : Ring<C>>(
                     }
             )
     /**
-     * Returns difference between the polynomial and the integer represented as polynomial.
+     * Returns difference between the polynomial and the integer represented as a polynomial.
      *
      * The operation is equivalent to subtraction [other] copies of unit polynomial from [this].
      */
@@ -97,22 +95,25 @@ public open class ListPolynomialSpace<C, A : Ring<C>>(
                     }
             )
     /**
-     * Returns product of the polynomial and the integer represented as polynomial.
+     * Returns product of the polynomial and the integer represented as a polynomial.
      *
      * The operation is equivalent to sum of [other] copies of [this].
      */
     public override operator fun ListPolynomial<C>.times(other: Int): ListPolynomial<C> =
-        if (other == 0) zero
-        else ListPolynomial(
+        when (other) {
+            0 -> zero
+            1 -> this
+            else -> ListPolynomial(
                 coefficients
                     .toMutableList()
                     .apply {
                         for (deg in indices) this[deg] = this[deg] * other
                     }
             )
+        }
 
     /**
-     * Returns sum of the integer represented as polynomial and the polynomial.
+     * Returns sum of the integer represented as a polynomial and the polynomial.
      *
      * The operation is equivalent to adding [this] copies of unit polynomial to [other].
      */
@@ -130,39 +131,44 @@ public open class ListPolynomialSpace<C, A : Ring<C>>(
                     }
             )
     /**
-     * Returns difference between the integer represented as polynomial and the polynomial.
+     * Returns difference between the integer represented as a polynomial and the polynomial.
      *
      * The operation is equivalent to subtraction [this] copies of unit polynomial from [other].
      */
     public override operator fun Int.minus(other: ListPolynomial<C>): ListPolynomial<C> =
-        if (this == 0) other
-        else
         ListPolynomial(
             other.coefficients
                 .toMutableList()
                 .apply {
-                        forEachIndexed { index, c -> if (index != 0) this[index] = -c }
+                    if (this@minus == 0) {
+                        indices.forEach { this[it] = -this[it] }
+                    } else {
+                        (1..lastIndex).forEach { this[it] = -this[it] }
 
                         val result = this@minus - getOrElse(0) { constantZero }
 
-                        if(size == 0) add(result)
+                        if (size == 0) add(result)
                         else this[0] = result
                     }
+                }
         )
     /**
-     * Returns product of the integer represented as polynomial and the polynomial.
+     * Returns product of the integer represented as a polynomial and the polynomial.
      *
      * The operation is equivalent to sum of [this] copies of [other].
      */
     public override operator fun Int.times(other: ListPolynomial<C>): ListPolynomial<C> =
-        if (this == 0) zero
-        else ListPolynomial(
+        when (this) {
+            0 -> zero
+            1 -> other
+            else -> ListPolynomial(
                 other.coefficients
                     .toMutableList()
                     .apply {
                         for (deg in indices) this[deg] = this@times * this[deg]
                     }
             )
+        }
 
     /**
      * Converts the integer [value] to polynomial.
@@ -170,7 +176,7 @@ public open class ListPolynomialSpace<C, A : Ring<C>>(
     public override fun number(value: Int): ListPolynomial<C> = number(constantNumber(value))
 
     /**
-     * Returns sum of the constant represented as polynomial and the polynomial.
+     * Returns sum of the constant represented as a polynomial and the polynomial.
      */
     public override operator fun C.plus(other: ListPolynomial<C>): ListPolynomial<C> =
         with(other.coefficients) {
@@ -186,7 +192,7 @@ public open class ListPolynomialSpace<C, A : Ring<C>>(
             )
         }
     /**
-     * Returns difference between the constant represented as polynomial and the polynomial.
+     * Returns difference between the constant represented as a polynomial and the polynomial.
      */
     public override operator fun C.minus(other: ListPolynomial<C>): ListPolynomial<C> =
         with(other.coefficients) {
@@ -194,7 +200,7 @@ public open class ListPolynomialSpace<C, A : Ring<C>>(
             else ListPolynomial(
                 toMutableList()
                     .apply {
-                        forEachIndexed { index, c -> if (index != 0) this[index] = -c }
+                        (1 .. lastIndex).forEach { this[it] = -this[it] }
 
                         val result = if (size == 0) this@minus else this@minus - get(0)
 
@@ -204,7 +210,7 @@ public open class ListPolynomialSpace<C, A : Ring<C>>(
             )
         }
     /**
-     * Returns product of the constant represented as polynomial and the polynomial.
+     * Returns product of the constant represented as a polynomial and the polynomial.
      */
     public override operator fun C.times(other: ListPolynomial<C>): ListPolynomial<C> =
         ListPolynomial(
@@ -216,7 +222,7 @@ public open class ListPolynomialSpace<C, A : Ring<C>>(
         )
 
     /**
-     * Returns sum of the constant represented as polynomial and the polynomial.
+     * Returns sum of the constant represented as a polynomial and the polynomial.
      */
     public override operator fun ListPolynomial<C>.plus(other: C): ListPolynomial<C> =
         with(coefficients) {
@@ -232,7 +238,7 @@ public open class ListPolynomialSpace<C, A : Ring<C>>(
             )
         }
     /**
-     * Returns difference between the constant represented as polynomial and the polynomial.
+     * Returns difference between the constant represented as a polynomial and the polynomial.
      */
     public override operator fun ListPolynomial<C>.minus(other: C): ListPolynomial<C> =
         with(coefficients) {
@@ -248,7 +254,7 @@ public open class ListPolynomialSpace<C, A : Ring<C>>(
             )
         }
     /**
-     * Returns product of the constant represented as polynomial and the polynomial.
+     * Returns product of the constant represented as a polynomial and the polynomial.
      */
     public override operator fun ListPolynomial<C>.times(other: C): ListPolynomial<C> =
         ListPolynomial(
@@ -262,7 +268,7 @@ public open class ListPolynomialSpace<C, A : Ring<C>>(
     /**
      * Converts the constant [value] to polynomial.
      */
-    public override fun number(value: C): ListPolynomial<C> = ListPolynomial(value)
+    public override fun number(value: C): ListPolynomial<C> = ListPolynomial(listOf(value))
 
     /**
      * Returns negation of the polynomial.
@@ -315,15 +321,19 @@ public open class ListPolynomialSpace<C, A : Ring<C>>(
             }
         )
     }
+    /**
+     * Raises [arg] to the integer power [exponent].
+     */ // TODO: To optimize boxing
+    override fun power(arg: ListPolynomial<C>, exponent: UInt): ListPolynomial<C> = super.power(arg, exponent)
 
     /**
      * Instance of zero polynomial (zero of the polynomial ring).
      */
     override val zero: ListPolynomial<C> = ListPolynomial(emptyList())
     /**
-     * Instance of unit constant (unit of the underlying ring).
+     * Instance of unit polynomial (unit of the polynomial ring).
      */
-    override val one: ListPolynomial<C> = ListPolynomial(listOf(constantOne))
+    override val one: ListPolynomial<C> by lazy { ListPolynomial(listOf(constantOne)) }
 
     /**
      * Degree of the polynomial, [see also](https://en.wikipedia.org/wiki/Degree_of_a_polynomial). If the polynomial is
@@ -331,25 +341,45 @@ public open class ListPolynomialSpace<C, A : Ring<C>>(
      */
     public override val ListPolynomial<C>.degree: Int get() = coefficients.lastIndex
 
-    @Suppress("NOTHING_TO_INLINE")
-    public inline fun ListPolynomial<C>.substitute(argument: C): C = this.substitute(ring, argument)
-    @Suppress("NOTHING_TO_INLINE")
-    public inline fun ListPolynomial<C>.substitute(argument: ListPolynomial<C>): ListPolynomial<C> = this.substitute(ring, argument)
-
-    @Suppress("NOTHING_TO_INLINE")
-    public inline fun ListPolynomial<C>.asFunction(): (C) -> C = { this.substitute(ring, it) }
-    @Suppress("NOTHING_TO_INLINE")
-    public inline fun ListPolynomial<C>.asFunctionOnConstants(): (C) -> C = { this.substitute(ring, it) }
-    @Suppress("NOTHING_TO_INLINE")
-    public inline fun ListPolynomial<C>.asFunctionOnPolynomials(): (ListPolynomial<C>) -> ListPolynomial<C> = { this.substitute(ring, it) }
-
+    // TODO: When context receivers will be ready move all of this substitutions and invocations to utilities with
+    //  [ListPolynomialSpace] as a context receiver
     /**
-     * Evaluates the polynomial for the given value [argument].
+     * Evaluates value of [this] polynomial on provided [argument].
      */
     @Suppress("NOTHING_TO_INLINE")
-    public inline operator fun ListPolynomial<C>.invoke(argument: C): C = this.substitute(ring, argument)
+    public inline fun ListPolynomial<C>.substitute(argument: C): C = substitute(ring, argument)
+    /**
+     * Substitutes provided polynomial [argument] into [this] polynomial.
+     */
     @Suppress("NOTHING_TO_INLINE")
-    public inline operator fun ListPolynomial<C>.invoke(argument: ListPolynomial<C>): ListPolynomial<C> = this.substitute(ring, argument)
+    public inline fun ListPolynomial<C>.substitute(argument: ListPolynomial<C>): ListPolynomial<C> = substitute(ring, argument)
+
+    /**
+     * Represent [this] polynomial as a regular context-less function.
+     */
+    @Suppress("NOTHING_TO_INLINE")
+    public inline fun ListPolynomial<C>.asFunction(): (C) -> C = asFunctionOver(ring)
+    /**
+     * Represent [this] polynomial as a regular context-less function.
+     */
+    @Suppress("NOTHING_TO_INLINE")
+    public inline fun ListPolynomial<C>.asFunctionOfConstant(): (C) -> C = asFunctionOfConstantOver(ring)
+    /**
+     * Represent [this] polynomial as a regular context-less function.
+     */
+    @Suppress("NOTHING_TO_INLINE")
+    public inline fun ListPolynomial<C>.asFunctionOfPolynomial(): (ListPolynomial<C>) -> ListPolynomial<C> = asFunctionOfPolynomialOver(ring)
+
+    /**
+     * Evaluates value of [this] polynomial on provided [argument].
+     */
+    @Suppress("NOTHING_TO_INLINE")
+    public inline operator fun ListPolynomial<C>.invoke(argument: C): C = substitute(ring, argument)
+    /**
+     * Evaluates value of [this] polynomial on provided [argument].
+     */
+    @Suppress("NOTHING_TO_INLINE")
+    public inline operator fun ListPolynomial<C>.invoke(argument: ListPolynomial<C>): ListPolynomial<C> = substitute(ring, argument)
 }
 
 /**

kmath-functions/src/commonMain/kotlin/space/kscience/kmath/functions/ListRationalFunction.kt

@@ -8,13 +8,23 @@ package space.kscience.kmath.functions
 import space.kscience.kmath.operations.Ring
 
 
+/**
+ * Represents univariate rational function that stores its numerator and denominator as [ListPolynomial]s.
+ */
 public data class ListRationalFunction<C>(
     public override val numerator: ListPolynomial<C>,
     public override val denominator: ListPolynomial<C>
 ) : RationalFunction<C, ListPolynomial<C>> {
-    override fun toString(): String = "RationalFunction${numerator.coefficients}/${denominator.coefficients}"
+    override fun toString(): String = "ListRationalFunction${numerator.coefficients}/${denominator.coefficients}"
 }
 
+/**
+ * Arithmetic context for univariate rational functions with numerator and denominator represented as [ListPolynomial]s.
+ *
+ * @param C the type of constants. Polynomials have them a coefficients in their terms.
+ * @param A type of provided underlying ring of constants. It's [Ring] of [C].
+ * @param ring underlying ring of constants of type [A].
+ */
 public class ListRationalFunctionSpace<C, A : Ring<C>> (
     public val ring: A,
 ) :
@@ -30,76 +40,98 @@ public class ListRationalFunctionSpace<C, A : Ring<C>> (
             ListRationalFunction<C>,
             >() {
 
+    /**
+     * Underlying polynomial ring. Its polynomial operations are inherited by local polynomial operations.
+     */
     override val polynomialRing : ListPolynomialSpace<C, A> = ListPolynomialSpace(ring)
+    /**
+     * Constructor of [ListRationalFunction] from numerator and denominator [ListPolynomial].
+     */
     override fun constructRationalFunction(numerator: ListPolynomial<C>, denominator: ListPolynomial<C>): ListRationalFunction<C> =
         ListRationalFunction(numerator, denominator)
 
+    // TODO: When context receivers will be ready move all of this substitutions and invocations to utilities with
+    //  [ListPolynomialSpace] as a context receiver
     /**
-     * Instance of zero rational function (zero of the rational functions ring).
+     * Evaluates value of [this] polynomial on provided argument.
      */
-    public override val zero: ListRationalFunction<C> = ListRationalFunction(polynomialZero, polynomialOne)
+    @Suppress("NOTHING_TO_INLINE")
+    public inline fun ListPolynomial<C>.substitute(argument: C): C = substitute(ring, argument)
     /**
-     * Instance of unit polynomial (unit of the rational functions ring).
+     * Substitutes provided polynomial [argument] into [this] polynomial.
      */
-    public override val one: ListRationalFunction<C> = ListRationalFunction(polynomialOne, polynomialOne)
+    @Suppress("NOTHING_TO_INLINE")
+    public inline fun ListPolynomial<C>.substitute(argument: ListPolynomial<C>): ListPolynomial<C> = substitute(ring, argument)
+    /**
+     * Substitutes provided rational function [argument] into [this] polynomial.
+     */
+    @Suppress("NOTHING_TO_INLINE")
+    public inline fun ListPolynomial<C>.substitute(argument: ListRationalFunction<C>): ListRationalFunction<C> = substitute(ring, argument)
+    /**
+     * Substitutes provided polynomial [argument] into [this] rational function.
+     */
+    @Suppress("NOTHING_TO_INLINE")
+    public inline fun ListRationalFunction<C>.substitute(argument: ListPolynomial<C>): ListRationalFunction<C> = substitute(ring, argument)
+    /**
+     * Substitutes provided rational function [argument] into [this] rational function.
+     */
+    @Suppress("NOTHING_TO_INLINE")
+    public inline fun ListRationalFunction<C>.substitute(argument: ListRationalFunction<C>): ListRationalFunction<C> = substitute(ring, argument)
 
-    // TODO: Разобрать
+    /**
+     * Represent [this] polynomial as a regular context-less function.
+     */
+    @Suppress("NOTHING_TO_INLINE")
+    public inline fun ListPolynomial<C>.asFunction(): (C) -> C = { substitute(ring, it) }
+    /**
+     * Represent [this] polynomial as a regular context-less function.
+     */
+    @Suppress("NOTHING_TO_INLINE")
+    public inline fun ListPolynomial<C>.asFunctionOfConstant(): (C) -> C = { substitute(ring, it) }
+    /**
+     * Represent [this] polynomial as a regular context-less function.
+     */
+    @Suppress("NOTHING_TO_INLINE")
+    public inline fun ListPolynomial<C>.asFunctionOfPolynomial(): (ListPolynomial<C>) -> ListPolynomial<C> = { substitute(ring, it) }
+    /**
+     * Represent [this] polynomial as a regular context-less function.
+     */
+    @Suppress("NOTHING_TO_INLINE")
+    public inline fun ListPolynomial<C>.asFunctionOfRationalFunction(): (ListRationalFunction<C>) -> ListRationalFunction<C> = { substitute(ring, it) }
+    /**
+     * Represent [this] rational function as a regular context-less function.
+     */
+    @Suppress("NOTHING_TO_INLINE")
+    public inline fun ListRationalFunction<C>.asFunctionOfPolynomial(): (ListPolynomial<C>) -> ListRationalFunction<C> = { substitute(ring, it) }
+    /**
+     * Represent [this] rational function as a regular context-less function.
+     */
+    @Suppress("NOTHING_TO_INLINE")
+    public inline fun ListRationalFunction<C>.asFunctionOfRationalFunction(): (ListRationalFunction<C>) -> ListRationalFunction<C> = { substitute(ring, it) }
 
-//    operator fun invoke(arg: UnivariatePolynomial<T>): RationalFunction<T> =
-//        RationalFunction(
-//            numerator(arg),
-//            denominator(arg)
-//        )
-//
-//    operator fun invoke(arg: RationalFunction<T>): RationalFunction<T> {
-//        val num = numerator invokeRFTakeNumerator arg
-//        val den = denominator invokeRFTakeNumerator arg
-//        val degreeDif = numeratorDegree - denominatorDegree
-//        return if (degreeDif > 0)
-//            RationalFunction(
-//                num,
-//                multiplyByPower(den, arg.denominator, degreeDif)
-//            )
-//        else
-//            RationalFunction(
-//                multiplyByPower(num, arg.denominator, -degreeDif),
-//                den
-//            )
-//    }
-//
-//    override fun toString(): String = toString(UnivariatePolynomial.variableName)
-//
-//    fun toString(withVariableName: String = UnivariatePolynomial.variableName): String =
-//        when(true) {
-//            numerator.isZero() -> "0"
-//            denominator.isOne() -> numerator.toString(withVariableName)
-//            else -> "${numerator.toStringWithBrackets(withVariableName)}/${denominator.toStringWithBrackets(withVariableName)}"
-//        }
-//
-//    fun toStringWithBrackets(withVariableName: String = UnivariatePolynomial.variableName): String =
-//        when(true) {
-//            numerator.isZero() -> "0"
-//            denominator.isOne() -> numerator.toStringWithBrackets(withVariableName)
-//            else -> "(${numerator.toStringWithBrackets(withVariableName)}/${denominator.toStringWithBrackets(withVariableName)})"
-//        }
-//
-//    fun toReversedString(withVariableName: String = UnivariatePolynomial.variableName): String =
-//        when(true) {
-//            numerator.isZero() -> "0"
-//            denominator.isOne() -> numerator.toReversedString(withVariableName)
-//            else -> "${numerator.toReversedStringWithBrackets(withVariableName)}/${denominator.toReversedStringWithBrackets(withVariableName)}"
-//        }
-//
-//    fun toReversedStringWithBrackets(withVariableName: String = UnivariatePolynomial.variableName): String =
-//        when(true) {
-//            numerator.isZero() -> "0"
-//            denominator.isOne() -> numerator.toReversedStringWithBrackets(withVariableName)
-//            else -> "(${numerator.toReversedStringWithBrackets(withVariableName)}/${denominator.toReversedStringWithBrackets(withVariableName)})"
-//        }
-//
-//    fun removeZeros() =
-//        RationalFunction(
-//            numerator.removeZeros(),
-//            denominator.removeZeros()
-//        )
+    /**
+     * Evaluates value of [this] polynomial on provided argument.
+     */
+    @Suppress("NOTHING_TO_INLINE")
+    public inline operator fun ListPolynomial<C>.invoke(argument: C): C = substitute(ring, argument)
+    /**
+     * Evaluates value of [this] polynomial on provided argument.
+     */
+    @Suppress("NOTHING_TO_INLINE")
+    public inline operator fun ListPolynomial<C>.invoke(argument: ListPolynomial<C>): ListPolynomial<C> = substitute(ring, argument)
+    /**
+     * Evaluates value of [this] polynomial on provided argument.
+     */
+    @Suppress("NOTHING_TO_INLINE")
+    public inline operator fun ListPolynomial<C>.invoke(argument: ListRationalFunction<C>): ListRationalFunction<C> = substitute(ring, argument)
+    /**
+     * Evaluates value of [this] rational function on provided argument.
+     */
+    @Suppress("NOTHING_TO_INLINE")
+    public inline operator fun ListRationalFunction<C>.invoke(argument: ListPolynomial<C>): ListRationalFunction<C> = substitute(ring, argument)
+    /**
+     * Evaluates value of [this] rational function on provided argument.
+     */
+    @Suppress("NOTHING_TO_INLINE")
+    public inline operator fun ListRationalFunction<C>.invoke(argument: ListRationalFunction<C>): ListRationalFunction<C> = substitute(ring, argument)
 }

kmath-functions/src/commonMain/kotlin/space/kscience/kmath/functions/NumberedPolynomial.kt

@@ -5,44 +5,43 @@
 
 package space.kscience.kmath.functions
 
-import space.kscience.kmath.operations.invoke
 import space.kscience.kmath.operations.Ring
-import space.kscience.kmath.operations.ScaleOperations
-import kotlin.contracts.InvocationKind
-import kotlin.contracts.contract
-import kotlin.experimental.ExperimentalTypeInference
+import space.kscience.kmath.structures.Buffer
 import kotlin.jvm.JvmName
 import kotlin.math.max
 
 
 /**
- * Polynomial model without fixation on specific context they are applied to.
+ * Represents multivariate polynomial that stores its coefficients in a [Map] and terms' signatures in a [List].
  *
  * @param C the type of constants.
  */
 public data class NumberedPolynomial<C>
+@PublishedApi
 internal constructor(
     /**
-     * Map that collects coefficients of the polynomial. Every monomial `a x_1^{d_1} ... x_n^{d_n}` is represented as
-     * pair "key-value" in the map, where value is coefficients `a` and
-     * key is list that associates index of every variable in the monomial with multiplicity of the variable occurring
-     * in the monomial. For example coefficients of polynomial `5 x_1^2 x_3^3 - 6 x_2` can be represented as
+     * Map that contains coefficients of the polynomial.
+     *
+     * Every monomial `a x_1^{d_1} ... x_n^{d_n}` is stored as a pair "key-value" in the map, where the value is the
+     * coefficient `a` and the key is a list that associates index of every variable in the monomial with their degree
+     * in the monomial. For example, coefficients of a polynomial `5 x_1^2 x_3^3 - 6 x_2` can be represented as
      * ```
      * mapOf(
-     *      listOf(2, 0, 3) to 5,
-     *      listOf(0, 1) to (-6),
+     *      listOf(2, 0, 3) to 5, // 5 x_1^2 x_3^3 +
+     *      listOf(0, 1) to (-6), // (-6) x_2^1
      * )
      * ```
      * and also as
      * ```
      * mapOf(
-     *      listOf(2, 0, 3) to 5,
-     *      listOf(0, 1) to (-6),
-     *      listOf(0, 1, 1) to 0,
+     *      listOf(2, 0, 3) to 5, // 5 x_1^2 x_3^3 +
+     *      listOf(0, 1) to (-6), // (-6) x_2^1
+     *      listOf(0, 1, 1) to 0, // 0 x_2^1 x_3^1
      * )
      * ```
-     * It is recommended not to put zero monomials into the map, but is not prohibited. Lists of degrees always do not
-     * contain any zeros on end, but can contain zeros on start or anywhere in middle.
+     * It is not prohibited to put extra zero monomials into the map (as for `0 x_2 x_3` in the example). But the
+     * bigger the coefficients map the worse performance of arithmetical operations performed on it. Thus, it is
+     * recommended not to put (or even to remove) extra (or useless) monomials in the coefficients map.
      */
     public val coefficients: Map<List<UInt>, C>
 ) : Polynomial<C> {
@@ -50,24 +49,25 @@ internal constructor(
 }
 
 /**
- * Space of polynomials.
+ * Arithmetic context for multivariate polynomials with coefficients stored as a [Map] and terms' signatures stored as a
+ * [List] constructed with the provided [ring] of constants.
  *
- * @param C the type of operated polynomials.
- * @param A the intersection of [Ring] of [C] and [ScaleOperations] of [C].
- * @param ring the [A] instance.
+ * @param C the type of constants. Polynomials have them a coefficients in their terms.
+ * @param A type of provided underlying ring of constants. It's [Ring] of [C].
+ * @param ring underlying ring of constants of type [A].
  */
-public open class NumberedPolynomialSpace<C, A : Ring<C>>(
-    public final override val ring: A,
+public class NumberedPolynomialSpace<C, A : Ring<C>>(
+    public override val ring: A,
 ) : PolynomialSpaceOverRing<C, NumberedPolynomial<C>, A> {
     /**
-     * Returns sum of the polynomial and the integer represented as polynomial.
+     * Returns sum of the polynomial and the integer represented as a polynomial.
      *
      * The operation is equivalent to adding [other] copies of unit polynomial to [this].
      */
     public override operator fun NumberedPolynomial<C>.plus(other: Int): NumberedPolynomial<C> =
         if (other == 0) this
         else
-            NumberedPolynomial(
+            NumberedPolynomialAsIs(
                 coefficients
                     .toMutableMap()
                     .apply {
@@ -77,14 +77,14 @@ public open class NumberedPolynomialSpace<C, A : Ring<C>>(
                     }
             )
     /**
-     * Returns difference between the polynomial and the integer represented as polynomial.
+     * Returns difference between the polynomial and the integer represented as a polynomial.
      *
      * The operation is equivalent to subtraction [other] copies of unit polynomial from [this].
      */
     public override operator fun NumberedPolynomial<C>.minus(other: Int): NumberedPolynomial<C> =
         if (other == 0) this
         else
-            NumberedPolynomial(
+            NumberedPolynomialAsIs(
                 coefficients
                     .toMutableMap()
                     .apply {
@@ -94,29 +94,32 @@ public open class NumberedPolynomialSpace<C, A : Ring<C>>(
                     }
             )
     /**
-     * Returns product of the polynomial and the integer represented as polynomial.
+     * Returns product of the polynomial and the integer represented as a polynomial.
      *
      * The operation is equivalent to sum of [other] copies of [this].
      */
     public override operator fun NumberedPolynomial<C>.times(other: Int): NumberedPolynomial<C> =
-        if (other == 0) zero
-        else NumberedPolynomial<C>(
+        when (other) {
+            0 -> zero
+            1 -> this
+            else -> NumberedPolynomialAsIs(
                 coefficients
                     .toMutableMap()
                     .apply {
                         for (degs in keys) this[degs] = this[degs]!! * other
                     }
             )
+        }
 
     /**
-     * Returns sum of the integer represented as polynomial and the polynomial.
+     * Returns sum of the integer represented as a polynomial and the polynomial.
      *
      * The operation is equivalent to adding [this] copies of unit polynomial to [other].
      */
     public override operator fun Int.plus(other: NumberedPolynomial<C>): NumberedPolynomial<C> =
         if (this == 0) other
         else
-            NumberedPolynomial(
+            NumberedPolynomialAsIs(
                 other.coefficients
                     .toMutableMap()
                     .apply {
@@ -126,36 +129,43 @@ public open class NumberedPolynomialSpace<C, A : Ring<C>>(
                     }
             )
     /**
-     * Returns difference between the integer represented as polynomial and the polynomial.
+     * Returns difference between the integer represented as a polynomial and the polynomial.
      *
      * The operation is equivalent to subtraction [this] copies of unit polynomial from [other].
      */
     public override operator fun Int.minus(other: NumberedPolynomial<C>): NumberedPolynomial<C> =
-        if (this == 0) other
-        else
-            NumberedPolynomial(
+        NumberedPolynomialAsIs(
             other.coefficients
                 .toMutableMap()
                 .apply {
+                    if (this@minus == 0) {
+                        forEach { (key, value) -> this[key] = -value }
+                    } else {
+                        forEach { (key, value) -> if (key.isNotEmpty()) this[key] = -value }
+
                         val degs = emptyList<UInt>()
 
                         this[degs] = this@minus - getOrElse(degs) { constantZero }
                     }
+                }
             )
     /**
-     * Returns product of the integer represented as polynomial and the polynomial.
+     * Returns product of the integer represented as a polynomial and the polynomial.
      *
      * The operation is equivalent to sum of [this] copies of [other].
      */
     public override operator fun Int.times(other: NumberedPolynomial<C>): NumberedPolynomial<C> =
-        if (this == 0) zero
-        else NumberedPolynomial(
+        when (this) {
+            0 -> zero
+            1 -> other
+            else -> NumberedPolynomialAsIs(
                 other.coefficients
                     .toMutableMap()
                     .apply {
                         for (degs in keys) this[degs] = this@times * this[degs]!!
                     }
             )
+        }
 
     /**
      * Converts the integer [value] to polynomial.
@@ -163,12 +173,12 @@ public open class NumberedPolynomialSpace<C, A : Ring<C>>(
     public override fun number(value: Int): NumberedPolynomial<C> = number(constantNumber(value))
 
     /**
-     * Returns sum of the constant represented as polynomial and the polynomial.
+     * Returns sum of the constant represented as a polynomial and the polynomial.
      */
     override operator fun C.plus(other: NumberedPolynomial<C>): NumberedPolynomial<C> =
         with(other.coefficients) {
-            if (isEmpty()) NumberedPolynomial<C>(mapOf(emptyList<UInt>() to this@plus))
-            else NumberedPolynomial<C>(
+            if (isEmpty()) NumberedPolynomialAsIs(mapOf(emptyList<UInt>() to this@plus))
+            else NumberedPolynomialAsIs(
                 toMutableMap()
                     .apply {
                         val degs = emptyList<UInt>()
@@ -178,15 +188,15 @@ public open class NumberedPolynomialSpace<C, A : Ring<C>>(
             )
         }
     /**
-     * Returns difference between the constant represented as polynomial and the polynomial.
+     * Returns difference between the constant represented as a polynomial and the polynomial.
      */
     override operator fun C.minus(other: NumberedPolynomial<C>): NumberedPolynomial<C> =
         with(other.coefficients) {
-            if (isEmpty()) NumberedPolynomial<C>(mapOf(emptyList<UInt>() to this@minus))
-            else NumberedPolynomial<C>(
+            if (isEmpty()) NumberedPolynomialAsIs(mapOf(emptyList<UInt>() to this@minus))
+            else NumberedPolynomialAsIs(
                 toMutableMap()
                     .apply {
-                        forEach { (degs, c) -> if(degs.isNotEmpty()) this[degs] = -c }
+                        forEach { (degs, c) -> if (degs.isNotEmpty()) this[degs] = -c }
 
                         val degs = emptyList<UInt>()
 
@@ -195,10 +205,10 @@ public open class NumberedPolynomialSpace<C, A : Ring<C>>(
             )
         }
     /**
-     * Returns product of the constant represented as polynomial and the polynomial.
+     * Returns product of the constant represented as a polynomial and the polynomial.
      */
     override operator fun C.times(other: NumberedPolynomial<C>): NumberedPolynomial<C> =
-        NumberedPolynomial<C>(
+        NumberedPolynomialAsIs(
             other.coefficients
                 .toMutableMap()
                 .apply {
@@ -207,12 +217,12 @@ public open class NumberedPolynomialSpace<C, A : Ring<C>>(
         )
 
     /**
-     * Returns sum of the constant represented as polynomial and the polynomial.
+     * Returns sum of the constant represented as a polynomial and the polynomial.
      */
     override operator fun NumberedPolynomial<C>.plus(other: C): NumberedPolynomial<C> =
         with(coefficients) {
-            if (isEmpty()) NumberedPolynomial<C>(mapOf(emptyList<UInt>() to other))
-            else NumberedPolynomial<C>(
+            if (isEmpty()) NumberedPolynomialAsIs(mapOf(emptyList<UInt>() to other))
+            else NumberedPolynomialAsIs(
                 toMutableMap()
                     .apply {
                         val degs = emptyList<UInt>()
@@ -222,12 +232,12 @@ public open class NumberedPolynomialSpace<C, A : Ring<C>>(
             )
         }
     /**
-     * Returns difference between the constant represented as polynomial and the polynomial.
+     * Returns difference between the constant represented as a polynomial and the polynomial.
      */
     override operator fun NumberedPolynomial<C>.minus(other: C): NumberedPolynomial<C> =
         with(coefficients) {
-            if (isEmpty()) NumberedPolynomial<C>(mapOf(emptyList<UInt>() to other))
-            else NumberedPolynomial<C>(
+            if (isEmpty()) NumberedPolynomialAsIs(mapOf(emptyList<UInt>() to other))
+            else NumberedPolynomialAsIs(
                 toMutableMap()
                     .apply {
                         val degs = emptyList<UInt>()
@@ -237,10 +247,10 @@ public open class NumberedPolynomialSpace<C, A : Ring<C>>(
             )
         }
     /**
-     * Returns product of the constant represented as polynomial and the polynomial.
+     * Returns product of the constant represented as a polynomial and the polynomial.
      */
     override operator fun NumberedPolynomial<C>.times(other: C): NumberedPolynomial<C> =
-        NumberedPolynomial<C>(
+        NumberedPolynomialAsIs(
             coefficients
                 .toMutableMap()
                 .apply {
@@ -252,22 +262,22 @@ public open class NumberedPolynomialSpace<C, A : Ring<C>>(
      * Converts the constant [value] to polynomial.
      */
     public override fun number(value: C): NumberedPolynomial<C> =
-        NumberedPolynomial(mapOf(emptyList<UInt>() to value))
+        NumberedPolynomialAsIs(mapOf(emptyList<UInt>() to value))
 
     /**
      * Returns negation of the polynomial.
      */
     override fun NumberedPolynomial<C>.unaryMinus(): NumberedPolynomial<C> =
-        NumberedPolynomial<C>(
+        NumberedPolynomialAsIs(
             coefficients.mapValues { -it.value }
         )
     /**
      * Returns sum of the polynomials.
      */
     override operator fun NumberedPolynomial<C>.plus(other: NumberedPolynomial<C>): NumberedPolynomial<C> =
-        NumberedPolynomial<C>(
+        NumberedPolynomialAsIs(
             buildMap(coefficients.size + other.coefficients.size) {
-                other.coefficients.mapValuesTo(this) { it.value }
+                coefficients.mapValuesTo(this) { it.value }
                 other.coefficients.mapValuesTo(this) { (key, value) -> if (key in this) this[key]!! + value else value }
             }
         )
@@ -275,9 +285,9 @@ public open class NumberedPolynomialSpace<C, A : Ring<C>>(
      * Returns difference of the polynomials.
      */
     override operator fun NumberedPolynomial<C>.minus(other: NumberedPolynomial<C>): NumberedPolynomial<C> =
-        NumberedPolynomial<C>(
+        NumberedPolynomialAsIs(
             buildMap(coefficients.size + other.coefficients.size) {
-                other.coefficients.mapValuesTo(this) { it.value }
+                coefficients.mapValuesTo(this) { it.value }
                 other.coefficients.mapValuesTo(this) { (key, value) -> if (key in this) this[key]!! - value else -value }
             }
         )
@@ -285,7 +295,7 @@ public open class NumberedPolynomialSpace<C, A : Ring<C>>(
      * Returns product of the polynomials.
      */
     override operator fun NumberedPolynomial<C>.times(other: NumberedPolynomial<C>): NumberedPolynomial<C> =
-        NumberedPolynomial<C>(
+        NumberedPolynomialAsIs(
             buildMap(coefficients.size * other.coefficients.size) {
                 for ((degs1, c1) in coefficients) for ((degs2, c2) in other.coefficients) {
                     val degs =
@@ -296,20 +306,25 @@ public open class NumberedPolynomialSpace<C, A : Ring<C>>(
                 }
             }
         )
+    /**
+     * Raises [arg] to the integer power [exponent].
+     */ // TODO: To optimize boxing
+    override fun power(arg: NumberedPolynomial<C>, exponent: UInt): NumberedPolynomial<C> = super.power(arg, exponent)
 
     /**
      * Instance of zero polynomial (zero of the polynomial ring).
      */
-    override val zero: NumberedPolynomial<C> = NumberedPolynomial<C>(emptyMap())
+    override val zero: NumberedPolynomial<C> = NumberedPolynomialAsIs(emptyMap())
     /**
      * Instance of unit polynomial (unit of the polynomial ring).
      */
-    override val one: NumberedPolynomial<C> =
-        NumberedPolynomial<C>(
+    override val one: NumberedPolynomial<C> by lazy {
+        NumberedPolynomialAsIs(
             mapOf(
                 emptyList<UInt>() to constantOne // 1 * x_1^0 * x_2^0 * ...
             )
         )
+    }
 
     /**
      * Maximal index (ID) of variable occurring in the polynomial with positive power. If there is no such variable,
@@ -365,25 +380,61 @@ public open class NumberedPolynomialSpace<C, A : Ring<C>>(
                 }
             }.count { it }
 
+    // TODO: When context receivers will be ready move all of this substitutions and invocations to utilities with
+    //  [ListPolynomialSpace] as a context receiver
+    /**
+     * Substitutes provided arguments [arguments] into [this] polynomial.
+     */
     @Suppress("NOTHING_TO_INLINE")
-    public inline fun NumberedPolynomial<C>.substitute(argument: Map<Int, C>): NumberedPolynomial<C> = this.substitute(ring, argument)
+    public inline fun NumberedPolynomial<C>.substitute(arguments: Map<Int, C>): NumberedPolynomial<C> = substitute(ring, arguments)
+    /**
+     * Substitutes provided arguments [arguments] into [this] polynomial.
+     */
     @Suppress("NOTHING_TO_INLINE")
     @JvmName("substitutePolynomial")
-    public inline fun NumberedPolynomial<C>.substitute(argument: Map<Int, NumberedPolynomial<C>>): NumberedPolynomial<C> = this.substitute(ring, argument)
+    public inline fun NumberedPolynomial<C>.substitute(arguments: Map<Int, NumberedPolynomial<C>>) : NumberedPolynomial<C> = substitute(ring, arguments)
+    /**
+     * Substitutes provided arguments [arguments] into [this] polynomial.
+     */
+    @Suppress("NOTHING_TO_INLINE")
+    public inline fun NumberedPolynomial<C>.substitute(arguments: Buffer<C>): NumberedPolynomial<C> = substitute(ring, arguments)
+    /**
+     * Substitutes provided arguments [arguments] into [this] polynomial.
+     */
+    @Suppress("NOTHING_TO_INLINE")
+    @JvmName("substitutePolynomial")
+    public inline fun NumberedPolynomial<C>.substitute(arguments: Buffer<NumberedPolynomial<C>>) : NumberedPolynomial<C> = substitute(ring, arguments)
+    /**
+     * Substitutes provided arguments [arguments] into [this] polynomial.
+     */
+    @Suppress("NOTHING_TO_INLINE")
+    public inline fun NumberedPolynomial<C>.substituteFully(arguments: Buffer<C>): C = this.substituteFully(ring, arguments)
 
+    /**
+     * Represent [this] polynomial as a regular context-less function.
+     */
     @Suppress("NOTHING_TO_INLINE")
-    public inline fun NumberedPolynomial<C>.asFunction(): (Map<Int, C>) -> NumberedPolynomial<C> = { this.substitute(ring, it) }
+    public inline fun NumberedPolynomial<C>.asFunction(): (Buffer<C>) -> C = asFunctionOver(ring)
+    /**
+     * Represent [this] polynomial as a regular context-less function.
+     */
     @Suppress("NOTHING_TO_INLINE")
-    public inline fun NumberedPolynomial<C>.asFunctionOnConstants(): (Map<Int, C>) -> NumberedPolynomial<C> = { this.substitute(ring, it) }
+    public inline fun NumberedPolynomial<C>.asFunctionOfConstant(): (Buffer<C>) -> C = asFunctionOfConstantOver(ring)
+    /**
+     * Represent [this] polynomial as a regular context-less function.
+     */
     @Suppress("NOTHING_TO_INLINE")
-    public inline fun NumberedPolynomial<C>.asFunctionOnPolynomials(): (Map<Int, NumberedPolynomial<C>>) -> NumberedPolynomial<C> = { this.substitute(ring, it) }
+    public inline fun NumberedPolynomial<C>.asFunctionOfPolynomial(): (Buffer<NumberedPolynomial<C>>) -> NumberedPolynomial<C> = asFunctionOfPolynomialOver(ring)
 
+    /**
+     * Evaluates value of [this] polynomial on provided [arguments].
+     */
     @Suppress("NOTHING_TO_INLINE")
-    public inline operator fun NumberedPolynomial<C>.invoke(argument: Map<Int, C>): NumberedPolynomial<C> = this.substitute(ring, argument)
+    public inline operator fun NumberedPolynomial<C>.invoke(arguments: Buffer<C>): C = substituteFully(ring, arguments)
+    /**
+     * Substitutes provided [arguments] into [this] polynomial.
+     */
     @Suppress("NOTHING_TO_INLINE")
     @JvmName("invokePolynomial")
-    public inline operator fun NumberedPolynomial<C>.invoke(argument: Map<Int, NumberedPolynomial<C>>): NumberedPolynomial<C> = this.substitute(ring, argument)
-
-    // FIXME: Move to other constructors with context receiver
-    public fun C.asNumberedPolynomial() : NumberedPolynomial<C> = NumberedPolynomial<C>(mapOf(emptyList<UInt>() to this))
+    public inline operator fun NumberedPolynomial<C>.invoke(arguments: Buffer<NumberedPolynomial<C>>): NumberedPolynomial<C> = substitute(ring, arguments)
 }

kmath-functions/src/commonMain/kotlin/space/kscience/kmath/functions/NumberedRationalFunction.kt

@@ -7,9 +7,14 @@ package space.kscience.kmath.functions
 
 import space.kscience.kmath.operations.Ring
 import space.kscience.kmath.operations.invoke
+import space.kscience.kmath.structures.Buffer
+import kotlin.jvm.JvmName
 import kotlin.math.max
 
 
+/**
+ * Represents multivariate rational function that stores its numerator and denominator as [NumberedPolynomial]s.
+ */
 public class NumberedRationalFunction<C> internal constructor(
     public override val numerator: NumberedPolynomial<C>,
     public override val denominator: NumberedPolynomial<C>
@@ -17,6 +22,13 @@ public class NumberedRationalFunction<C> internal constructor(
     override fun toString(): String = "NumberedRationalFunction${numerator.coefficients}/${denominator.coefficients}"
 }
 
+/**
+ * Arithmetic context for univariate rational functions with numerator and denominator represented as [NumberedPolynomial]s.
+ *
+ * @param C the type of constants. Polynomials have them a coefficients in their terms.
+ * @param A type of provided underlying ring of constants. It's [Ring] of [C].
+ * @param ring underlying ring of constants of type [A].
+ */
 public class NumberedRationalFunctionSpace<C, A: Ring<C>> (
     public val ring: A,
 ) :
@@ -32,22 +44,19 @@ public class NumberedRationalFunctionSpace<C, A: Ring<C>> (
             NumberedRationalFunction<C>,
             >() {
 
-    override val polynomialRing : NumberedPolynomialSpace<C, A> = NumberedPolynomialSpace(ring)
-    override fun constructRationalFunction(
+    /**
+     * Underlying polynomial ring. Its polynomial operations are inherited by local polynomial operations.
+     */
+    public override val polynomialRing : NumberedPolynomialSpace<C, A> = NumberedPolynomialSpace(ring)
+    /**
+     * Constructor of rational functions (of type [NumberedRationalFunction]) from numerator and denominator (of type [NumberedPolynomial]).
+     */
+    protected override fun constructRationalFunction(
         numerator: NumberedPolynomial<C>,
         denominator: NumberedPolynomial<C>
     ): NumberedRationalFunction<C> =
         NumberedRationalFunction(numerator, denominator)
 
-    /**
-     * Instance of zero rational function (zero of the rational functions ring).
-     */
-    public override val zero: NumberedRationalFunction<C> = NumberedRationalFunction(polynomialZero, polynomialOne)
-    /**
-     * Instance of unit polynomial (unit of the rational functions ring).
-     */
-    public override val one: NumberedRationalFunction<C> = NumberedRationalFunction(polynomialOne, polynomialOne)
-
     /**
      * Maximal index (ID) of variable occurring in the polynomial with positive power. If there is no such variable,
      * the result is `-1`.
@@ -99,90 +108,140 @@ public class NumberedRationalFunctionSpace<C, A: Ring<C>> (
                 }
             }.count { it }
 
-    // TODO: Разобрать
+    // TODO: When context receivers will be ready move all of this substitutions and invocations to utilities with
+    //  [ListPolynomialSpace] as a context receiver
+    /**
+     * Substitutes provided constant [argument] into [this] polynomial.
+     */
+    @Suppress("NOTHING_TO_INLINE")
+    public inline fun NumberedPolynomial<C>.substitute(argument: Map<Int, C>): NumberedPolynomial<C> = substitute(ring, argument)
+    /**
+     * Substitutes provided polynomial [argument] into [this] polynomial.
+     */
+    @Suppress("NOTHING_TO_INLINE")
+    @JvmName("substitutePolynomial")
+    public inline fun NumberedPolynomial<C>.substitute(argument: Map<Int, NumberedPolynomial<C>>): NumberedPolynomial<C> = substitute(ring, argument)
+    /**
+     * Substitutes provided rational function [argument] into [this] polynomial.
+     */
+    @Suppress("NOTHING_TO_INLINE")
+    @JvmName("substituteRationalFunction")
+    public inline fun NumberedPolynomial<C>.substitute(argument: Map<Int, NumberedRationalFunction<C>>): NumberedRationalFunction<C> = substitute(ring, argument)
+    /**
+     * Substitutes provided constant [argument] into [this] rational function.
+     */
+    @Suppress("NOTHING_TO_INLINE")
+    public inline fun NumberedRationalFunction<C>.substitute(argument: Map<Int, C>): NumberedRationalFunction<C> = substitute(ring, argument)
+    /**
+     * Substitutes provided polynomial [argument] into [this] rational function.
+     */
+    @Suppress("NOTHING_TO_INLINE")
+    @JvmName("substitutePolynomial")
+    public inline fun NumberedRationalFunction<C>.substitute(argument: Map<Int, NumberedPolynomial<C>>): NumberedRationalFunction<C> = substitute(ring, argument)
+    /**
+     * Substitutes provided rational function [argument] into [this] rational function.
+     */
+    @Suppress("NOTHING_TO_INLINE")
+    @JvmName("substituteRationalFunction")
+    public inline fun NumberedRationalFunction<C>.substitute(argument: Map<Int, NumberedRationalFunction<C>>): NumberedRationalFunction<C> = substitute(ring, argument)
+    /**
+     * Substitutes provided constant [argument] into [this] polynomial.
+     */
+    @Suppress("NOTHING_TO_INLINE")
+    public inline fun NumberedPolynomial<C>.substitute(argument: Buffer<C>): NumberedPolynomial<C> = substitute(ring, argument)
+    /**
+     * Substitutes provided polynomial [argument] into [this] polynomial.
+     */
+    @Suppress("NOTHING_TO_INLINE")
+    @JvmName("substitutePolynomial")
+    public inline fun NumberedPolynomial<C>.substitute(argument: Buffer<NumberedPolynomial<C>>): NumberedPolynomial<C> = substitute(ring, argument)
+    /**
+     * Substitutes provided rational function [argument] into [this] polynomial.
+     */
+    @Suppress("NOTHING_TO_INLINE")
+    @JvmName("substituteRationalFunction")
+    public inline fun NumberedPolynomial<C>.substitute(argument: Buffer<NumberedRationalFunction<C>>): NumberedRationalFunction<C> = substitute(ring, argument)
+    /**
+     * Substitutes provided constant [argument] into [this] rational function.
+     */
+    @Suppress("NOTHING_TO_INLINE")
+    public inline fun NumberedRationalFunction<C>.substitute(argument: Buffer<C>): NumberedRationalFunction<C> = substitute(ring, argument)
+    /**
+     * Substitutes provided polynomial [arguments] into [this] rational function.
+     */
+    @Suppress("NOTHING_TO_INLINE")
+    @JvmName("substitutePolynomial")
+    public inline fun NumberedRationalFunction<C>.substitute(arguments: Buffer<NumberedPolynomial<C>>): NumberedRationalFunction<C> = substitute(ring, arguments)
+    /**
+     * Substitutes provided rational function [arguments] into [this] rational function.
+     */
+    @Suppress("NOTHING_TO_INLINE")
+    @JvmName("substituteRationalFunction")
+    public inline fun NumberedRationalFunction<C>.substitute(arguments: Buffer<NumberedRationalFunction<C>>): NumberedRationalFunction<C> = substitute(ring, arguments)
+    /**
+     * Substitutes provided constant [arguments] into [this] polynomial.
+     */
+    @Suppress("NOTHING_TO_INLINE")
+    public inline fun NumberedPolynomial<C>.substituteFully(arguments: Buffer<C>): C = substituteFully(ring, arguments)
 
-//    operator fun invoke(arg: Map<Int, C>): NumberedRationalFunction<C> =
-//        NumberedRationalFunction(
-//            numerator(arg),
-//            denominator(arg)
-//        )
-//
-//    @JvmName("invokePolynomial")
-//    operator fun invoke(arg: Map<Int, Polynomial<C>>): NumberedRationalFunction<C> =
-//        NumberedRationalFunction(
-//            numerator(arg),
-//            denominator(arg)
-//        )
-//
-//    @JvmName("invokeRationalFunction")
-//    operator fun invoke(arg: Map<Int, NumberedRationalFunction<C>>): NumberedRationalFunction<C> {
-//        var num = numerator invokeRFTakeNumerator arg
-//        var den = denominator invokeRFTakeNumerator arg
-//        for (variable in 0 until max(numerator.countOfVariables, denominator.countOfVariables)) if (variable in arg) {
-//            val degreeDif = numerator.degrees.getOrElse(variable) { 0 } - denominator.degrees.getOrElse(variable) { 0 }
-//            if (degreeDif > 0)
-//                den = multiplyByPower(den, arg[variable]!!.denominator, degreeDif)
-//            else
-//                num = multiplyByPower(num, arg[variable]!!.denominator, -degreeDif)
-//        }
-//        return NumberedRationalFunction(num, den)
-//    }
-//
-//    override fun toString(): String = toString(Polynomial.variableName)
-//
-//    fun toString(withVariableName: String = Polynomial.variableName): String =
-//        when(true) {
-//            numerator.isZero() -> "0"
-//            denominator.isOne() -> numerator.toString(withVariableName)
-//            else -> "${numerator.toStringWithBrackets(withVariableName)}/${denominator.toStringWithBrackets(withVariableName)}"
-//        }
-//
-//    fun toString(namer: (Int) -> String): String =
-//        when(true) {
-//            numerator.isZero() -> "0"
-//            denominator.isOne() -> numerator.toString(namer)
-//            else -> "${numerator.toStringWithBrackets(namer)}/${denominator.toStringWithBrackets(namer)}"
-//        }
-//
-//    fun toStringWithBrackets(withVariableName: String = Polynomial.variableName): String =
-//        when(true) {
-//            numerator.isZero() -> "0"
-//            denominator.isOne() -> numerator.toStringWithBrackets(withVariableName)
-//            else -> "(${numerator.toStringWithBrackets(withVariableName)}/${denominator.toStringWithBrackets(withVariableName)})"
-//        }
-//
-//    fun toStringWithBrackets(namer: (Int) -> String): String =
-//        when(true) {
-//            numerator.isZero() -> "0"
-//            denominator.isOne() -> numerator.toStringWithBrackets(namer)
-//            else -> "(${numerator.toStringWithBrackets(namer)}/${denominator.toStringWithBrackets(namer)})"
-//        }
-//
-//    fun toReversedString(withVariableName: String = Polynomial.variableName): String =
-//        when(true) {
-//            numerator.isZero() -> "0"
-//            denominator.isOne() -> numerator.toReversedString(withVariableName)
-//            else -> "${numerator.toReversedStringWithBrackets(withVariableName)}/${denominator.toReversedStringWithBrackets(withVariableName)}"
-//        }
-//
-//    fun toReversedString(namer: (Int) -> String): String =
-//        when(true) {
-//            numerator.isZero() -> "0"
-//            denominator.isOne() -> numerator.toReversedString(namer)
-//            else -> "${numerator.toReversedStringWithBrackets(namer)}/${denominator.toReversedStringWithBrackets(namer)}"
-//        }
-//
-//    fun toReversedStringWithBrackets(withVariableName: String = Polynomial.variableName): String =
-//        when(true) {
-//            numerator.isZero() -> "0"
-//            denominator.isOne() -> numerator.toReversedStringWithBrackets(withVariableName)
-//            else -> "(${numerator.toReversedStringWithBrackets(withVariableName)}/${denominator.toReversedStringWithBrackets(withVariableName)})"
-//        }
-//
-//    fun toReversedStringWithBrackets(namer: (Int) -> String): String =
-//        when(true) {
-//            numerator.isZero() -> "0"
-//            denominator.isOne() -> numerator.toReversedStringWithBrackets(namer)
-//            else -> "(${numerator.toReversedStringWithBrackets(namer)}/${denominator.toReversedStringWithBrackets(namer)})"
-//        }
+    /**
+     * Represent [this] polynomial as a regular context-less function.
+     */
+    @Suppress("NOTHING_TO_INLINE")
+    public inline fun NumberedPolynomial<C>.asFunction(): (Buffer<C>) -> C = asFunctionOver(ring)
+    /**
+     * Represent [this] polynomial as a regular context-less function.
+     */
+    @Suppress("NOTHING_TO_INLINE")
+    public inline fun NumberedPolynomial<C>.asFunctionOfConstant(): (Buffer<C>) -> C = asFunctionOfConstantOver(ring)
+    /**
+     * Represent [this] polynomial as a regular context-less function.
+     */
+    @Suppress("NOTHING_TO_INLINE")
+    public inline fun NumberedPolynomial<C>.asFunctionOfPolynomial(): (Buffer<NumberedPolynomial<C>>) -> NumberedPolynomial<C> = asFunctionOfPolynomialOver(ring)
+    /**
+     * Represent [this] polynomial as a regular context-less function.
+     */
+    @Suppress("NOTHING_TO_INLINE")
+    public inline fun NumberedPolynomial<C>.asFunctionOfRationalFunction(): (Buffer<NumberedRationalFunction<C>>) -> NumberedRationalFunction<C> = asFunctionOfRationalFunctionOver(ring)
+    /**
+     * Represent [this] polynomial as a regular context-less function.
+     */
+    @Suppress("NOTHING_TO_INLINE")
+    public inline fun NumberedRationalFunction<C>.asFunctionOfPolynomial(): (Buffer<NumberedPolynomial<C>>) -> NumberedRationalFunction<C> = asFunctionOfPolynomialOver(ring)
+    /**
+     * Represent [this] polynomial as a regular context-less function.
+     */
+    @Suppress("NOTHING_TO_INLINE")
+    public inline fun NumberedRationalFunction<C>.asFunctionOfRationalFunction(): (Buffer<NumberedRationalFunction<C>>) -> NumberedRationalFunction<C> = asFunctionOfRationalFunctionOver(ring)
+
+    /**
+     * Evaluates value of [this] polynomial on provided [arguments].
+     */
+    @Suppress("NOTHING_TO_INLINE")
+    public inline operator fun NumberedPolynomial<C>.invoke(arguments: Buffer<C>): C = substituteFully(ring, arguments)
+    /**
+     * Substitutes provided [arguments] into [this] polynomial.
+     */
+    @Suppress("NOTHING_TO_INLINE")
+    @JvmName("invokePolynomial")
+    public inline operator fun NumberedPolynomial<C>.invoke(arguments: Buffer<NumberedPolynomial<C>>): NumberedPolynomial<C> = substitute(ring, arguments)
+    /**
+     * Substitutes provided [arguments] into [this] polynomial.
+     */
+    @Suppress("NOTHING_TO_INLINE")
+    @JvmName("invokeRationalFunction")
+    public inline operator fun NumberedPolynomial<C>.invoke(arguments: Buffer<NumberedRationalFunction<C>>): NumberedRationalFunction<C> = substitute(ring, arguments)
+    /**
+     * Substitutes provided [arguments] into [this] rational function.
+     */
+    @Suppress("NOTHING_TO_INLINE")
+    @JvmName("invokePolynomial")
+    public inline operator fun NumberedRationalFunction<C>.invoke(arguments: Buffer<NumberedPolynomial<C>>): NumberedRationalFunction<C> = substitute(ring, arguments)
+    /**
+     * Substitutes provided [arguments] into [this] rational function.
+     */
+    @Suppress("NOTHING_TO_INLINE")
+    @JvmName("invokeRationalFunction")
+    public inline operator fun NumberedRationalFunction<C>.invoke(arguments: Buffer<NumberedRationalFunction<C>>): NumberedRationalFunction<C> = substitute(ring, arguments)
 }

kmath-functions/src/commonMain/kotlin/space/kscience/kmath/functions/Polynomial.kt

@@ -25,38 +25,38 @@ public interface Polynomial<C>
 @Suppress("INAPPLICABLE_JVM_NAME", "PARAMETER_NAME_CHANGED_ON_OVERRIDE") // FIXME: Waiting for KT-31420
 public interface PolynomialSpace<C, P: Polynomial<C>> : Ring<P> {
     /**
-     * Returns sum of the constant and the integer represented as constant (member of underlying ring).
+     * Returns sum of the constant and the integer represented as a constant (member of underlying ring).
      *
      * The operation is equivalent to adding [other] copies of unit of underlying ring to [this].
      */
     public operator fun C.plus(other: Int): C
     /**
-     * Returns difference between the constant and the integer represented as constant (member of underlying ring).
+     * Returns difference between the constant and the integer represented as a constant (member of underlying ring).
      *
      * The operation is equivalent to subtraction [other] copies of unit of underlying ring from [this].
      */
     public operator fun C.minus(other: Int): C
     /**
-     * Returns product of the constant and the integer represented as constant (member of underlying ring).
+     * Returns product of the constant and the integer represented as a constant (member of underlying ring).
      *
      * The operation is equivalent to sum of [other] copies of [this].
      */
     public operator fun C.times(other: Int): C
 
     /**
-     * Returns sum of the integer represented as constant (member of underlying ring) and the constant.
+     * Returns sum of the integer represented as a constant (member of underlying ring) and the constant.
      *
      * The operation is equivalent to adding [this] copies of unit of underlying ring to [other].
      */
     public operator fun Int.plus(other: C): C
     /**
-     * Returns difference between the integer represented as constant (member of underlying ring) and the constant.
+     * Returns difference between the integer represented as a constant (member of underlying ring) and the constant.
      *
      * The operation is equivalent to subtraction [this] copies of unit of underlying ring from [other].
      */
     public operator fun Int.minus(other: C): C
     /**
-     * Returns product of the integer represented as constant (member of underlying ring) and the constant.
+     * Returns product of the integer represented as a constant (member of underlying ring) and the constant.
      *
      * The operation is equivalent to sum of [this] copies of [other].
      */
@@ -72,38 +72,38 @@ public interface PolynomialSpace<C, P: Polynomial<C>> : Ring<P> {
     public fun Int.asConstant(): C = constantNumber(this)
 
     /**
-     * Returns sum of the polynomial and the integer represented as polynomial.
+     * Returns sum of the polynomial and the integer represented as a polynomial.
      *
      * The operation is equivalent to adding [other] copies of unit polynomial to [this].
      */
     public operator fun P.plus(other: Int): P = addMultipliedByDoubling(this, one, other)
     /**
-     * Returns difference between the polynomial and the integer represented as polynomial.
+     * Returns difference between the polynomial and the integer represented as a polynomial.
      *
      * The operation is equivalent to subtraction [other] copies of unit polynomial from [this].
      */
     public operator fun P.minus(other: Int): P = addMultipliedByDoubling(this, one, -other)
     /**
-     * Returns product of the polynomial and the integer represented as polynomial.
+     * Returns product of the polynomial and the integer represented as a polynomial.
      *
      * The operation is equivalent to sum of [other] copies of [this].
      */
     public operator fun P.times(other: Int): P = multiplyByDoubling(this, other)
 
     /**
-     * Returns sum of the integer represented as polynomial and the polynomial.
+     * Returns sum of the integer represented as a polynomial and the polynomial.
      *
      * The operation is equivalent to adding [this] copies of unit polynomial to [other].
      */
     public operator fun Int.plus(other: P): P = addMultipliedByDoubling(other, one, this)
     /**
-     * Returns difference between the integer represented as polynomial and the polynomial.
+     * Returns difference between the integer represented as a polynomial and the polynomial.
      *
      * The operation is equivalent to subtraction [this] copies of unit polynomial from [other].
      */
     public operator fun Int.minus(other: P): P = addMultipliedByDoubling(-other, one, this)
     /**
-     * Returns product of the integer represented as polynomial and the polynomial.
+     * Returns product of the integer represented as a polynomial and the polynomial.
      *
      * The operation is equivalent to sum of [this] copies of [other].
      */
@@ -165,28 +165,28 @@ public interface PolynomialSpace<C, P: Polynomial<C>> : Ring<P> {
     public val constantOne: C
 
     /**
-     * Returns sum of the constant represented as polynomial and the polynomial.
+     * Returns sum of the constant represented as a polynomial and the polynomial.
      */
     public operator fun C.plus(other: P): P
     /**
-     * Returns difference between the constant represented as polynomial and the polynomial.
+     * Returns difference between the constant represented as a polynomial and the polynomial.
      */
     public operator fun C.minus(other: P): P
     /**
-     * Returns product of the constant represented as polynomial and the polynomial.
+     * Returns product of the constant represented as a polynomial and the polynomial.
      */
     public operator fun C.times(other: P): P
 
     /**
-     * Returns sum of the constant represented as polynomial and the polynomial.
+     * Returns sum of the constant represented as a polynomial and the polynomial.
      */
     public operator fun P.plus(other: C): P
     /**
-     * Returns difference between the constant represented as polynomial and the polynomial.
+     * Returns difference between the constant represented as a polynomial and the polynomial.
      */
     public operator fun P.minus(other: C): P
     /**
-     * Returns product of the constant represented as polynomial and the polynomial.
+     * Returns product of the constant represented as a polynomial and the polynomial.
      */
     public operator fun P.times(other: C): P
 
@@ -254,41 +254,44 @@ public interface PolynomialSpace<C, P: Polynomial<C>> : Ring<P> {
 @Suppress("INAPPLICABLE_JVM_NAME") // FIXME: Waiting for KT-31420
 public interface PolynomialSpaceOverRing<C, P: Polynomial<C>, A: Ring<C>> : PolynomialSpace<C, P> {
 
+    /**
+     * Underlying ring of constants. Its operations on constants are inherited by local operations on constants.
+     */
     public val ring: A
 
     /**
-     * Returns sum of the constant and the integer represented as constant (member of underlying ring).
+     * Returns sum of the constant and the integer represented as a constant (member of underlying ring).
      *
      * The operation is equivalent to adding [other] copies of unit of underlying ring to [this].
      */
     public override operator fun C.plus(other: Int): C = ring { addMultipliedByDoubling(this@plus, one, other) }
     /**
-     * Returns difference between the constant and the integer represented as constant (member of underlying ring).
+     * Returns difference between the constant and the integer represented as a constant (member of underlying ring).
      *
      * The operation is equivalent to subtraction [other] copies of unit of underlying ring from [this].
      */
     public override operator fun C.minus(other: Int): C = ring { addMultipliedByDoubling(this@minus, one, -other) }
     /**
-     * Returns product of the constant and the integer represented as constant (member of underlying ring).
+     * Returns product of the constant and the integer represented as a constant (member of underlying ring).
      *
      * The operation is equivalent to sum of [other] copies of [this].
      */
     public override operator fun C.times(other: Int): C = ring { multiplyByDoubling(this@times, other) }
 
     /**
-     * Returns sum of the integer represented as constant (member of underlying ring) and the constant.
+     * Returns sum of the integer represented as a constant (member of underlying ring) and the constant.
      *
      * The operation is equivalent to adding [this] copies of unit of underlying ring to [other].
      */
     public override operator fun Int.plus(other: C): C = ring { addMultipliedByDoubling(other, one, this@plus) }
     /**
-     * Returns difference between the integer represented as constant (member of underlying ring) and the constant.
+     * Returns difference between the integer represented as a constant (member of underlying ring) and the constant.
      *
      * The operation is equivalent to subtraction [this] copies of unit of underlying ring from [other].
      */
     public override operator fun Int.minus(other: C): C = ring { addMultipliedByDoubling(-other, one, this@minus) }
     /**
-     * Returns product of the integer represented as constant (member of underlying ring) and the constant.
+     * Returns product of the integer represented as a constant (member of underlying ring) and the constant.
      *
      * The operation is equivalent to sum of [this] copies of [other].
      */
@@ -330,58 +333,145 @@ public interface PolynomialSpaceOverRing<C, P: Polynomial<C>, A: Ring<C>> : Poly
     public override val constantOne: C get() = ring.one
 }
 
+/**
+ * Abstraction of ring of polynomials of type [P] of variables of type [V] and over ring of constants of type [C].
+ *
+ * @param C the type of constants. Polynomials have them as coefficients in their terms.
+ * @param V the type of variables. Polynomials have them in representations of terms.
+ * @param P the type of polynomials.
+ */
 @Suppress("INAPPLICABLE_JVM_NAME") // FIXME: Waiting for KT-31420
 public interface MultivariatePolynomialSpace<C, V, P: Polynomial<C>>: PolynomialSpace<C, P> {
+    /**
+     * Returns sum of the variable represented as a monic monomial and the integer represented as a constant polynomial.
+     */
     @JvmName("plusVariableInt")
     public operator fun V.plus(other: Int): P
+    /**
+     * Returns difference between the variable represented as a monic monomial and the integer represented as a constant polynomial.
+     */
     @JvmName("minusVariableInt")
     public operator fun V.minus(other: Int): P
+    /**
+     * Returns product of the variable represented as a monic monomial and the integer represented as a constant polynomial.
+     */
     @JvmName("timesVariableInt")
     public operator fun V.times(other: Int): P
 
+    /**
+     * Returns sum of the integer represented as a constant polynomial and the variable represented as a monic monomial.
+     */
     @JvmName("plusIntVariable")
     public operator fun Int.plus(other: V): P
+    /**
+     * Returns difference between the integer represented as a constant polynomial and the variable represented as a monic monomial.
+     */
     @JvmName("minusIntVariable")
     public operator fun Int.minus(other: V): P
+    /**
+     * Returns product of the integer represented as a constant polynomial and the variable represented as a monic monomial.
+     */
     @JvmName("timesIntVariable")
     public operator fun Int.times(other: V): P
 
-    @JvmName("plusConstantVariable")
-    public operator fun C.plus(other: V): P
-    @JvmName("minusConstantVariable")
-    public operator fun C.minus(other: V): P
-    @JvmName("timesConstantVariable")
-    public operator fun C.times(other: V): P
-
+    /**
+     * Returns sum of the variable represented as a monic monomial and the constant represented as a constant polynomial.
+     */
     @JvmName("plusVariableConstant")
     public operator fun V.plus(other: C): P
+    /**
+     * Returns difference between the variable represented as a monic monomial and the constant represented as a constant polynomial.
+     */
     @JvmName("minusVariableConstant")
     public operator fun V.minus(other: C): P
+    /**
+     * Returns product of the variable represented as a monic monomial and the constant represented as a constant polynomial.
+     */
     @JvmName("timesVariableConstant")
     public operator fun V.times(other: C): P
 
+    /**
+     * Returns sum of the constant represented as a constant polynomial and the variable represented as a monic monomial.
+     */
+    @JvmName("plusConstantVariable")
+    public operator fun C.plus(other: V): P
+    /**
+     * Returns difference between the constant represented as a constant polynomial and the variable represented as a monic monomial.
+     */
+    @JvmName("minusConstantVariable")
+    public operator fun C.minus(other: V): P
+    /**
+     * Returns product of the constant represented as a constant polynomial and the variable represented as a monic monomial.
+     */
+    @JvmName("timesConstantVariable")
+    public operator fun C.times(other: V): P
+
+    /**
+     * Represents the variable as a monic monomial.
+     */
     @JvmName("unaryPlusVariable")
     public operator fun V.unaryPlus(): P
+    /**
+     * Returns negation of representation of the variable as a monic monomial.
+     */
     @JvmName("unaryMinusVariable")
     public operator fun V.unaryMinus(): P
+    /**
+     * Returns sum of the variables represented as monic monomials.
+     */
     @JvmName("plusVariableVariable")
     public operator fun V.plus(other: V): P
+    /**
+     * Returns difference between the variables represented as monic monomials.
+     */
     @JvmName("minusVariableVariable")
     public operator fun V.minus(other: V): P
+    /**
+     * Returns product of the variables represented as monic monomials.
+     */
     @JvmName("timesVariableVariable")
     public operator fun V.times(other: V): P
 
+    /**
+     * Represents the [variable] as a monic monomial.
+     */
+    @JvmName("numberVariable")
+    public fun number(variable: V): P = +variable
+    /**
+     * Represents the variable as a monic monomial.
+     */
+    @JvmName("asPolynomialVariable")
+    public fun V.asPolynomial(): P = number(this)
+
+    /**
+     * Returns sum of the variable represented as a monic monomial and the polynomial.
+     */
     @JvmName("plusVariablePolynomial")
     public operator fun V.plus(other: P): P
+    /**
+     * Returns difference between the variable represented as a monic monomial and the polynomial.
+     */
     @JvmName("minusVariablePolynomial")
     public operator fun V.minus(other: P): P
+    /**
+     * Returns product of the variable represented as a monic monomial and the polynomial.
+     */
     @JvmName("timesVariablePolynomial")
     public operator fun V.times(other: P): P
 
+    /**
+     * Returns sum of the polynomial and the variable represented as a monic monomial.
+     */
     @JvmName("plusPolynomialVariable")
     public operator fun P.plus(other: V): P
+    /**
+     * Returns difference between the polynomial and the variable represented as a monic monomial.
+     */
     @JvmName("minusPolynomialVariable")
     public operator fun P.minus(other: V): P
+    /**
+     * Returns product of the polynomial and the variable represented as a monic monomial.
+     */
     @JvmName("timesPolynomialVariable")
     public operator fun P.times(other: V): P
 

kmath-functions/src/commonMain/kotlin/space/kscience/kmath/functions/labeledConstructors.kt

@@ -3,6 +3,8 @@
  * Use of this source code is governed by the Apache 2.0 license that can be found in the license/LICENSE.txt file.
  */
 
+@file:Suppress("FunctionName", "NOTHING_TO_INLINE")
+
 package space.kscience.kmath.functions
 
 import space.kscience.kmath.expressions.Symbol
@@ -15,189 +17,502 @@ import space.kscience.kmath.operations.Ring
  */
 internal fun Map<Symbol, UInt>.cleanUp() = filterValues { it > 0U }
 
-// Waiting for context receivers :( FIXME: Replace with context receivers when they will be available
+/**
+ * Constructs [LabeledPolynomial] with provided coefficients map [coefs]. The map is used as is.
+ */
+@PublishedApi
+internal inline fun <C> LabeledPolynomialAsIs(coefs: Map<Map<Symbol, UInt>, C>) : LabeledPolynomial<C> = LabeledPolynomial<C>(coefs)
 
-@Suppress("FunctionName", "NOTHING_TO_INLINE")
-internal inline fun <C, A: Ring<C>> LabeledPolynomialSpace<C, A>.LabeledPolynomial(coefs: Map<Map<Symbol, UInt>, C>, toCheckInput: Boolean = true) : LabeledPolynomial<C> = ring.LabeledPolynomial(coefs, toCheckInput)
-@Suppress("FunctionName", "NOTHING_TO_INLINE")
-internal inline fun <C, A: Ring<C>> LabeledRationalFunctionSpace<C, A>.LabeledPolynomial(coefs: Map<Map<Symbol, UInt>, C>, toCheckInput: Boolean = true) : LabeledPolynomial<C> = ring.LabeledPolynomial(coefs, toCheckInput)
-@Suppress("FunctionName")
-internal fun <C, A: Ring<C>> A.LabeledPolynomial(coefs: Map<Map<Symbol, UInt>, C>, toCheckInput: Boolean = true) : LabeledPolynomial<C> {
-    if (!toCheckInput) return LabeledPolynomial<C>(coefs)
+/**
+ * Constructs [LabeledPolynomial] with provided collection of [pairs] of pairs "term's signature &mdash; term's coefficient".
+ * The collections will be transformed to map with [toMap] and then will be used as is.
+ */
+@PublishedApi
+internal inline fun <C> LabeledPolynomialAsIs(pairs: Collection<Pair<Map<Symbol, UInt>, C>>) : LabeledPolynomial<C> = LabeledPolynomial<C>(pairs.toMap())
 
-    val fixedCoefs = LinkedHashMap<Map<Symbol, UInt>, C>(coefs.size)
+/**
+ * Constructs [LabeledPolynomial] with provided array of [pairs] of pairs "term's signature &mdash; term's coefficient".
+ * The array will be transformed to map with [toMap] and then will be used as is.
+ */
+@PublishedApi
+internal inline fun <C> LabeledPolynomialAsIs(vararg pairs: Pair<Map<Symbol, UInt>, C>) : LabeledPolynomial<C> = LabeledPolynomial<C>(pairs.toMap())
+
+/**
+ * Constructs [LabeledPolynomial] with provided coefficients map [coefs]. The map is used as is.
+ *
+ * **Be sure you read description of [LabeledPolynomial.coefficients]. Otherwise, you may make a mistake that will
+ * cause wrong computation result or even runtime error.**
+ */
+@DelicatePolynomialAPI
+public inline fun <C> LabeledPolynomialWithoutCheck(coefs: Map<Map<Symbol, UInt>, C>) : LabeledPolynomial<C> = LabeledPolynomial<C>(coefs)
+
+/**
+ * Constructs [LabeledPolynomial] with provided collection of [pairs] of pairs "term's signature &mdash; term's coefficient".
+ * The collections will be transformed to map with [toMap] and then will be used as is.
+ *
+ * **Be sure you read description of [LabeledPolynomial.coefficients]. Otherwise, you may make a mistake that will
+ * cause wrong computation result or even runtime error.**
+ */
+@DelicatePolynomialAPI
+public inline fun <C> LabeledPolynomialWithoutCheck(pairs: Collection<Pair<Map<Symbol, UInt>, C>>) : LabeledPolynomial<C> = LabeledPolynomial<C>(pairs.toMap())
+
+/**
+ * Constructs [LabeledPolynomial] with provided array of [pairs] of pairs "term's signature &mdash; term's coefficient".
+ * The array will be transformed to map with [toMap] and then will be used as is.
+ *
+ * **Be sure you read description of [LabeledPolynomial.coefficients]. Otherwise, you may make a mistake that will
+ * cause wrong computation result or even runtime error.**
+ */
+@DelicatePolynomialAPI
+public inline fun <C> LabeledPolynomialWithoutCheck(vararg pairs: Pair<Map<Symbol, UInt>, C>) : LabeledPolynomial<C> = LabeledPolynomial<C>(pairs.toMap())
+
+/**
+ * Constructs [LabeledPolynomial] with provided coefficients map [coefs].
+ *
+ * [coefs] will be "cleaned up":
+ * 1. Zeros at the ends of terms' signatures (e.g. [coefs] keys) will be removed. (See [cleanUp].)
+ * 1. Terms that happen to have the same signature will be summed up.
+ * 1. New map will be formed of resulting terms.
+ */
+public fun <C> LabeledPolynomial(coefs: Map<Map<Symbol, UInt>, C>, add: (C, C) -> C) : LabeledPolynomial<C> {
+    val fixedCoefs = mutableMapOf<Map<Symbol, UInt>, C>()
 
     for (entry in coefs) {
         val key = entry.key.cleanUp()
         val value = entry.value
-        fixedCoefs[key] = if (key in fixedCoefs) fixedCoefs[key]!! + value else value
+        fixedCoefs[key] = if (key in fixedCoefs) add(fixedCoefs[key]!!, value) else value
     }
 
     return LabeledPolynomial<C>(fixedCoefs)
 }
 
-@Suppress("FunctionName", "NOTHING_TO_INLINE")
-internal inline fun <C, A: Ring<C>> LabeledPolynomialSpace<C, A>.LabeledPolynomial(pairs: Collection<Pair<Map<Symbol, UInt>, C>>, toCheckInput: Boolean = true) : LabeledPolynomial<C> = ring.LabeledPolynomial(pairs, toCheckInput)
-@Suppress("FunctionName", "NOTHING_TO_INLINE")
-internal inline fun <C, A: Ring<C>> LabeledRationalFunctionSpace<C, A>.LabeledPolynomial(pairs: Collection<Pair<Map<Symbol, UInt>, C>>, toCheckInput: Boolean = true) : LabeledPolynomial<C> = ring.LabeledPolynomial(pairs, toCheckInput)
-@Suppress("FunctionName")
-internal fun <C, A: Ring<C>> A.LabeledPolynomial(pairs: Collection<Pair<Map<Symbol, UInt>, C>>, toCheckInput: Boolean = true) : LabeledPolynomial<C> {
-    if (!toCheckInput) return LabeledPolynomial<C>(pairs.toMap())
-
-    val fixedCoefs = LinkedHashMap<Map<Symbol, UInt>, C>(pairs.size)
+/**
+ * Constructs [LabeledPolynomial] with provided collection of [pairs] of pairs "term's signature &mdash; term's coefficient".
+ *
+ * [pairs] will be "cleaned up":
+ * 1. Zeros at the ends of terms' signatures (e.g. [pairs] keys) will be removed. (See [cleanUp].)
+ * 1. Terms that happen to have the same signature will be summed up.
+ * 1. New map will be formed of resulting terms.
+ */
+public fun <C> LabeledPolynomial(pairs: Collection<Pair<Map<Symbol, UInt>, C>>, add: (C, C) -> C) : LabeledPolynomial<C> {
+    val fixedCoefs = mutableMapOf<Map<Symbol, UInt>, C>()
 
     for (entry in pairs) {
         val key = entry.first.cleanUp()
         val value = entry.second
-        fixedCoefs[key] = if (key in fixedCoefs) fixedCoefs[key]!! + value else value
+        fixedCoefs[key] = if (key in fixedCoefs) add(fixedCoefs[key]!!, value) else value
     }
 
     return LabeledPolynomial<C>(fixedCoefs)
 }
 
-@Suppress("FunctionName", "NOTHING_TO_INLINE")
-internal inline fun <C, A: Ring<C>> LabeledPolynomialSpace<C, A>.LabeledPolynomial(vararg pairs: Pair<Map<Symbol, UInt>, C>, toCheckInput: Boolean = true) : LabeledPolynomial<C> = ring.LabeledPolynomial(pairs = pairs, toCheckInput = toCheckInput)
-@Suppress("FunctionName", "NOTHING_TO_INLINE")
-internal inline fun <C, A: Ring<C>> LabeledRationalFunctionSpace<C, A>.LabeledPolynomial(vararg pairs: Pair<Map<Symbol, UInt>, C>, toCheckInput: Boolean = true) : LabeledPolynomial<C> = ring.LabeledPolynomial(pairs = pairs, toCheckInput = toCheckInput)
-@Suppress("FunctionName")
-internal fun <C, A: Ring<C>> A.LabeledPolynomial(vararg pairs: Pair<Map<Symbol, UInt>, C>, toCheckInput: Boolean = true) : LabeledPolynomial<C> {
-    if (!toCheckInput) return LabeledPolynomial<C>(pairs.toMap())
-
-    val fixedCoefs = LinkedHashMap<Map<Symbol, UInt>, C>(pairs.size)
+/**
+ * Constructs [LabeledPolynomial] with provided array [pairs] of pairs "term's signature &mdash; term's coefficient".
+ *
+ * [pairs] will be "cleaned up":
+ * 1. Zeros at the ends of terms' signatures (e.g. [pairs] keys) will be removed. (See [cleanUp].)
+ * 1. Terms that happen to have the same signature will be summed up.
+ * 1. New map will be formed of resulting terms.
+ */
+public fun <C> LabeledPolynomial(vararg pairs: Pair<Map<Symbol, UInt>, C>, add: (C, C) -> C) : LabeledPolynomial<C> {
+    val fixedCoefs = mutableMapOf<Map<Symbol, UInt>, C>()
 
     for (entry in pairs) {
         val key = entry.first.cleanUp()
         val value = entry.second
-        fixedCoefs[key] = if (key in fixedCoefs) fixedCoefs[key]!! + value else value
+        fixedCoefs[key] = if (key in fixedCoefs) add(fixedCoefs[key]!!, value) else value
     }
 
     return LabeledPolynomial<C>(fixedCoefs)
 }
 
-@Suppress("FunctionName")
-public fun <C, A: Ring<C>> A.LabeledPolynomial(coefs: Map<Map<Symbol, UInt>, C>) : LabeledPolynomial<C> = LabeledPolynomial(coefs, toCheckInput = true)
-@Suppress("FunctionName")
-public fun <C, A: Ring<C>> LabeledPolynomialSpace<C, A>.LabeledPolynomial(coefs: Map<Map<Symbol, UInt>, C>) : LabeledPolynomial<C> = LabeledPolynomial(coefs, toCheckInput = true)
-@Suppress("FunctionName")
-public fun <C, A: Ring<C>> LabeledRationalFunctionSpace<C, A>.LabeledPolynomial(coefs: Map<Map<Symbol, UInt>, C>) : LabeledPolynomial<C> = LabeledPolynomial(coefs, toCheckInput = true)
+// Waiting for context receivers :( FIXME: Replace with context receivers when they will be available
 
-@Suppress("FunctionName")
-public fun <C, A: Ring<C>> A.LabeledPolynomial(pairs: Collection<Pair<Map<Symbol, UInt>, C>>) : LabeledPolynomial<C> = LabeledPolynomial(pairs, toCheckInput = true)
-@Suppress("FunctionName")
-public fun <C, A: Ring<C>> LabeledPolynomialSpace<C, A>.LabeledPolynomial(pairs: Collection<Pair<Map<Symbol, UInt>, C>>) : LabeledPolynomial<C> = LabeledPolynomial(pairs, toCheckInput = true)
-@Suppress("FunctionName")
-public fun <C, A: Ring<C>> LabeledRationalFunctionSpace<C, A>.LabeledPolynomial(pairs: Collection<Pair<Map<Symbol, UInt>, C>>) : LabeledPolynomial<C> = LabeledPolynomial(pairs, toCheckInput = true)
+/**
+ * Constructs [LabeledPolynomial] with provided coefficients map [coefs].
+ *
+ * [coefs] will be "cleaned up":
+ * 1. Zeros at the ends of terms' signatures (e.g. [coefs] keys) will be removed. (See [cleanUp].)
+ * 1. Terms that happen to have the same signature will be summed up.
+ * 1. New map will be formed of resulting terms.
+ */
+public inline fun <C, A: Ring<C>> A.LabeledPolynomial(coefs: Map<Map<Symbol, UInt>, C>) : LabeledPolynomial<C> = LabeledPolynomial(coefs, ::add)
+/**
+ * Constructs [LabeledPolynomial] with provided coefficients map [coefs].
+ *
+ * [coefs] will be "cleaned up":
+ * 1. Zeros at the ends of terms' signatures (e.g. [coefs] keys) will be removed. (See [cleanUp].)
+ * 1. Terms that happen to have the same signature will be summed up.
+ * 1. New map will be formed of resulting terms.
+ */
+public inline fun <C, A: Ring<C>> LabeledPolynomialSpace<C, A>.LabeledPolynomial(coefs: Map<Map<Symbol, UInt>, C>) : LabeledPolynomial<C> = LabeledPolynomial(coefs) { left: C, right: C -> left + right }
 
-@Suppress("FunctionName")
-public fun <C, A: Ring<C>> A.LabeledPolynomial(vararg pairs: Pair<Map<Symbol, UInt>, C>) : LabeledPolynomial<C> = LabeledPolynomial(*pairs, toCheckInput = true)
-@Suppress("FunctionName")
-public fun <C, A: Ring<C>> LabeledPolynomialSpace<C, A>.LabeledPolynomial(vararg pairs: Pair<Map<Symbol, UInt>, C>) : LabeledPolynomial<C> = LabeledPolynomial(*pairs, toCheckInput = true)
-@Suppress("FunctionName")
-public fun <C, A: Ring<C>> LabeledRationalFunctionSpace<C, A>.LabeledPolynomial(vararg pairs: Pair<Map<Symbol, UInt>, C>) : LabeledPolynomial<C> = LabeledPolynomial(*pairs, toCheckInput = true)
+/**
+ * Constructs [LabeledPolynomial] with provided coefficients map [coefs].
+ *
+ * [coefs] will be "cleaned up":
+ * 1. Zeros at the ends of terms' signatures (e.g. [coefs] keys) will be removed. (See [cleanUp].)
+ * 1. Terms that happen to have the same signature will be summed up.
+ * 1. New map will be formed of resulting terms.
+ */
+public inline fun <C, A: Ring<C>> LabeledRationalFunctionSpace<C, A>.LabeledPolynomial(coefs: Map<Map<Symbol, UInt>, C>) : LabeledPolynomial<C> = LabeledPolynomial(coefs) { left: C, right: C -> left + right }
 
+/**
+ * Constructs [LabeledPolynomial] with provided collection of [pairs] of pairs "term's signature &mdash; term's coefficient".
+ *
+ * [pairs] will be "cleaned up":
+ * 1. Zeros at the ends of terms' signatures (e.g. [pairs] keys) will be removed. (See [cleanUp].)
+ * 1. Terms that happen to have the same signature will be summed up.
+ * 1. New map will be formed of resulting terms.
+ */
+public inline fun <C, A: Ring<C>> A.LabeledPolynomial(pairs: Collection<Pair<Map<Symbol, UInt>, C>>) : LabeledPolynomial<C> = LabeledPolynomial(pairs, ::add)
+
+/**
+ * Constructs [LabeledPolynomial] with provided collection of [pairs] of pairs "term's signature &mdash; term's coefficient".
+ *
+ * [pairs] will be "cleaned up":
+ * 1. Zeros at the ends of terms' signatures (e.g. [pairs] keys) will be removed. (See [cleanUp].)
+ * 1. Terms that happen to have the same signature will be summed up.
+ * 1. New map will be formed of resulting terms.
+ */
+public inline fun <C, A: Ring<C>> LabeledPolynomialSpace<C, A>.LabeledPolynomial(pairs: Collection<Pair<Map<Symbol, UInt>, C>>) : LabeledPolynomial<C> = LabeledPolynomial(pairs) { left: C, right: C -> left + right }
+/**
+ * Constructs [LabeledPolynomial] with provided collection of [pairs] of pairs "term's signature &mdash; term's coefficient".
+ *
+ * [pairs] will be "cleaned up":
+ * 1. Zeros at the ends of terms' signatures (e.g. [pairs] keys) will be removed. (See [cleanUp].)
+ * 1. Terms that happen to have the same signature will be summed up.
+ * 1. New map will be formed of resulting terms.
+ */
+public inline fun <C, A: Ring<C>> LabeledRationalFunctionSpace<C, A>.LabeledPolynomial(pairs: Collection<Pair<Map<Symbol, UInt>, C>>) : LabeledPolynomial<C> = LabeledPolynomial(pairs) { left: C, right: C -> left + right }
+
+/**
+ * Constructs [LabeledPolynomial] with provided array [pairs] of pairs "term's signature &mdash; term's coefficient".
+ *
+ * [pairs] will be "cleaned up":
+ * 1. Zeros at the ends of terms' signatures (e.g. [pairs] keys) will be removed. (See [cleanUp].)
+ * 1. Terms that happen to have the same signature will be summed up.
+ * 1. New map will be formed of resulting terms.
+ */
+public inline fun <C, A: Ring<C>> A.LabeledPolynomial(vararg pairs: Pair<Map<Symbol, UInt>, C>) : LabeledPolynomial<C> = LabeledPolynomial(*pairs) { left: C, right: C -> left + right }
+/**
+ * Constructs [LabeledPolynomial] with provided array [pairs] of pairs "term's signature &mdash; term's coefficient".
+ *
+ * [pairs] will be "cleaned up":
+ * 1. Zeros at the ends of terms' signatures (e.g. [pairs] keys) will be removed. (See [cleanUp].)
+ * 1. Terms that happen to have the same signature will be summed up.
+ * 1. New map will be formed of resulting terms.
+ */
+public inline fun <C, A: Ring<C>> LabeledPolynomialSpace<C, A>.LabeledPolynomial(vararg pairs: Pair<Map<Symbol, UInt>, C>) : LabeledPolynomial<C> = LabeledPolynomial(*pairs) { left: C, right: C -> left + right }
+/**
+ * Constructs [LabeledPolynomial] with provided array [pairs] of pairs "term's signature &mdash; term's coefficient".
+ *
+ * [pairs] will be "cleaned up":
+ * 1. Zeros at the ends of terms' signatures (e.g. [pairs] keys) will be removed. (See [cleanUp].)
+ * 1. Terms that happen to have the same signature will be summed up.
+ * 1. New map will be formed of resulting terms.
+ */
+public inline fun <C, A: Ring<C>> LabeledRationalFunctionSpace<C, A>.LabeledPolynomial(vararg pairs: Pair<Map<Symbol, UInt>, C>) : LabeledPolynomial<C> = LabeledPolynomial(*pairs) { left: C, right: C -> left + right }
+
+/**
+ * Converts [this] constant to [LabeledPolynomial].
+ */
+public inline fun <C> C.asLabeledPolynomial() : LabeledPolynomial<C> = LabeledPolynomialAsIs(mapOf(emptyMap<Symbol, UInt>() to this))
+
+///**
+//// * Converts [this] variable to [LabeledPolynomial].
+//// */
 //context(A)
-//public fun <C, A: Ring<C>> Symbol.asLabeledPolynomial() : LabeledPolynomial<C> = LabeledPolynomial<C>(mapOf(mapOf(this to 1u) to one))
+//public inline fun <C, A: Ring<C>> Symbol.asLabeledPolynomial() : LabeledPolynomial<C> = LabeledPolynomial<C>(mapOf(mapOf(this to 1u) to one))
+///**
+// * Converts [this] variable to [LabeledPolynomial].
+// */
 //context(LabeledPolynomialSpace<C, A>)
-//public fun <C, A: Ring<C>> Symbol.asLabeledPolynomial() : LabeledPolynomial<C> = LabeledPolynomial<C>(mapOf(mapOf(this to 1u) to constantOne))
+//public inline fun <C, A: Ring<C>> Symbol.asLabeledPolynomial() : LabeledPolynomial<C> = LabeledPolynomial<C>(mapOf(mapOf(this to 1u) to constantOne))
+///**
+// * Converts [this] variable to [LabeledPolynomial].
+// */
 //context(LabeledRationalFunctionSpace<C, A>)
-//public fun <C, A: Ring<C>> Symbol.asLabeledPolynomial() : LabeledPolynomial<C> = LabeledPolynomial<C>(mapOf(mapOf(this to 1u) to constantOne))
-
-public fun <C> C.asLabeledPolynomial() : LabeledPolynomial<C> = LabeledPolynomial<C>(mapOf(emptyMap<Symbol, UInt>() to this))
+//public inline fun <C, A: Ring<C>> Symbol.asLabeledPolynomial() : LabeledPolynomial<C> = LabeledPolynomial<C>(mapOf(mapOf(this to 1u) to constantOne))
 
+/**
+ * Marks DSL that allows to more simply create [LabeledPolynomial]s with good performance.
+ *
+ * For example, polynomial `5 a^2 c^3 - 6 b` can be described as
+ * ```
+ * Int.algebra {
+ *     val numberedPolynomial : NumberedPolynomial<Int> = NumberedPolynomial {
+ *         5 { a inPowerOf 2u; c inPowerOf 3u } // 5 a^2 c^3 +
+ *         (-6) { b inPowerOf 1u }              // (-6) b^1
+ *     }
+ * }
+ * ```
+ */
 @DslMarker
 @UnstableKMathAPI
 internal annotation class LabeledPolynomialConstructorDSL
 
+/**
+ * Builder of [LabeledPolynomial] signature. It should be used as an implicit context for lambdas that describe term signature.
+ */
 @UnstableKMathAPI
 @LabeledPolynomialConstructorDSL
 public class LabeledPolynomialTermSignatureBuilder {
+    /**
+     * Signature storage. Any declaration of any variable's power updates the storage by increasing corresponding value.
+     * Afterward the storage will be used as a resulting signature.
+     */
     private val signature: MutableMap<Symbol, UInt> = LinkedHashMap()
-    public fun build(): Map<Symbol, UInt> = signature
+
+    /**
+     * Builds the resulting signature.
+     *
+     * In fact, it just returns [signature] as regular signature of type `List<UInt>`.
+     */
+    @PublishedApi
+    internal fun build(): Map<Symbol, UInt> = signature
+
+    /**
+     * Declares power of [this] variable of degree [deg].
+     *
+     * Declaring another power of the same variable will increase its degree by received degree.
+     */
     public infix fun Symbol.inPowerOf(deg: UInt) {
         signature[this] = deg
     }
+    /**
+     * Declares power of [this] variable of degree [deg].
+     *
+     * Declaring another power of the same variable will increase its degree by received degree.
+     */
     @Suppress("NOTHING_TO_INLINE")
     public inline infix fun Symbol.pow(deg: UInt): Unit = this inPowerOf deg
+    /**
+     * Declares power of [this] variable of degree [deg].
+     *
+     * Declaring another power of the same variable will increase its degree by received degree.
+     */
     @Suppress("NOTHING_TO_INLINE")
     public inline infix fun Symbol.`in`(deg: UInt): Unit = this inPowerOf deg
+    /**
+     * Declares power of [this] variable of degree [deg].
+     *
+     * Declaring another power of the same variable will increase its degree by received degree.
+     */
     @Suppress("NOTHING_TO_INLINE")
     public inline infix fun Symbol.of(deg: UInt): Unit = this inPowerOf deg
 }
 
+/**
+ * Builder of [LabeledPolynomial]. It should be used as an implicit context for lambdas that describe [LabeledPolynomial].
+ */
 @UnstableKMathAPI
-public class LabeledPolynomialBuilder<C>(private val zero: C, private val add: (C, C) -> C, capacity: Int = 0) {
-    private val coefficients: MutableMap<Map<Symbol, UInt>, C> = LinkedHashMap(capacity)
-    public fun build(): LabeledPolynomial<C> = LabeledPolynomial<C>(coefficients)
-    public operator fun C.invoke(block: LabeledPolynomialTermSignatureBuilder.() -> Unit) {
-        val signature = LabeledPolynomialTermSignatureBuilder().apply(block).build()
-        coefficients[signature] = add(coefficients.getOrElse(signature) { zero }, this@invoke)
+public class LabeledPolynomialBuilder<C>(
+    /**
+     * Summation operation that will be used to sum coefficients of monomials of same signatures.
+     */
+    private val add: (C, C) -> C,
+    /**
+     * Initial capacity of coefficients map.
+     */
+    initialCapacity: Int = 0
+) {
+    /**
+     * Coefficients storage. Any declaration of any monomial updates the storage.
+     * Afterward the storage will be used as a resulting coefficients map.
+     */
+    private val coefficients: MutableMap<Map<Symbol, UInt>, C> = LinkedHashMap(initialCapacity)
+
+    /**
+     * Builds the resulting coefficients map.
+     *
+     * In fact, it just returns [coefficients] as regular coefficients map of type `Map<List<UInt>, C>`.
+     */
+    @PublishedApi
+    internal fun build(): LabeledPolynomial<C> = LabeledPolynomial<C>(coefficients)
+
+    /**
+     * Declares monomial with [this] coefficient and provided [signature].
+     *
+     * Declaring another monomial with the same signature will add [this] coefficient to existing one. If the sum of such
+     * coefficients is zero at any moment the monomial won't be removed but will be left as it is.
+     */
+    public infix fun C.with(signature: Map<Symbol, UInt>) {
+        coefficients[signature] = if (signature in coefficients) add(coefficients[signature]!!, this@with) else this@with
     }
+    /**
+     * Declares monomial with [this] coefficient and signature constructed by [block].
+     *
+     * Declaring another monomial with the same signature will add [this] coefficient to existing one. If the sum of such
+     * coefficients is zero at any moment the monomial won't be removed but will be left as it is.
+     */
     @Suppress("NOTHING_TO_INLINE")
     public inline infix fun C.with(noinline block: LabeledPolynomialTermSignatureBuilder.() -> Unit): Unit = this.invoke(block)
-    @Suppress("NOTHING_TO_INLINE")
-    public inline infix fun (LabeledPolynomialTermSignatureBuilder.() -> Unit).with(coef: C): Unit = coef.invoke(this)
-    @Suppress("NOTHING_TO_INLINE")
-    public infix fun sig(block: LabeledPolynomialTermSignatureBuilder.() -> Unit): LabeledPolynomialTermSignatureBuilder.() -> Unit = block
+    /**
+     * Declares monomial with [this] coefficient and signature constructed by [block].
+     *
+     * Declaring another monomial with the same signature will add [this] coefficient to existing one. If the sum of such
+     * coefficients is zero at any moment the monomial won't be removed but will be left as it is.
+     */
+    public inline operator fun C.invoke(block: LabeledPolynomialTermSignatureBuilder.() -> Unit): Unit =
+        this with LabeledPolynomialTermSignatureBuilder().apply(block).build()
 }
 
 // Waiting for context receivers :( FIXME: Replace with context receivers when they will be available
 
+///**
+// * Creates [LabeledPolynomial] with lambda [block] in context of [this] ring of constants.
+// *
+// * For example, polynomial `5 x_1^2 x_3^3 - 6 x_2` can be described as
+// * ```
+// * Int.algebra {
+// *     val LabeledPolynomial : LabeledPolynomial<Int> = LabeledPolynomial {
+// *         5 { 1 inPowerOf 2u; 3 inPowerOf 3u } // 5 x_1^2 x_3^3 +
+// *         (-6) { 2 inPowerOf 1u }              // (-6) x_2^1
+// *     }
+// * }
+// * ```
+// */
+// FIXME: For now this fabric does not let next two fabrics work. (See KT-52803.) Possible feature solutions:
+//  1. `LowPriorityInOverloadResolution` becomes public. Then it should be applied to this function.
+//  2. Union types are implemented. Then all three functions should be rewritten
+//     as one with single union type as a (context) receiver.
+//@UnstableKMathAPI
+//public inline fun <C, A: Ring<C>> A.LabeledPolynomial(initialCapacity: Int = 0, block: LabeledPolynomialBuilder<C>.() -> Unit) : LabeledPolynomial<C> = LabeledPolynomialBuilder(::add, initialCapacity).apply(block).build()
+/**
+ * Creates [LabeledPolynomial] with lambda [block] in context of [this] ring of [LabeledPolynomial]s.
+ *
+ * For example, polynomial `5 x_1^2 x_3^3 - 6 x_2` can be described as
+ * ```
+ * Int.algebra {
+ *     val LabeledPolynomial : LabeledPolynomial<Int> = LabeledPolynomial {
+ *         5 { 1 inPowerOf 2u; 3 inPowerOf 3u } // 5 x_1^2 x_3^3 +
+ *         (-6) { 2 inPowerOf 1u }              // (-6) x_2^1
+ *     }
+ * }
+ * ```
+ */
 @UnstableKMathAPI
-@LabeledPolynomialConstructorDSL
-@Suppress("FunctionName")
-public inline fun <C, A: Ring<C>> A.LabeledPolynomial(block: LabeledPolynomialBuilder<C>.() -> Unit) : LabeledPolynomial<C> = LabeledPolynomialBuilder(zero, ::add).apply(block).build()
+public inline fun <C, A: Ring<C>> LabeledPolynomialSpace<C, A>.LabeledPolynomial(initialCapacity: Int = 0, block: LabeledPolynomialBuilder<C>.() -> Unit) : LabeledPolynomial<C> = LabeledPolynomialBuilder({ left: C, right: C -> left + right }, initialCapacity).apply(block).build()
+/**
+ * Creates [LabeledPolynomial] with lambda [block] in context of [this] field of [LabeledRationalFunction]s.
+ *
+ * For example, polynomial `5 x_1^2 x_3^3 - 6 x_2` can be described as
+ * ```
+ * Int.algebra {
+ *     val LabeledPolynomial : LabeledPolynomial<Int> = LabeledPolynomial {
+ *         5 { 1 inPowerOf 2u; 3 inPowerOf 3u } // 5 x_1^2 x_3^3 +
+ *         (-6) { 2 inPowerOf 1u }              // (-6) x_2^1
+ *     }
+ * }
+ * ```
+ */
 @UnstableKMathAPI
-@LabeledPolynomialConstructorDSL
-@Suppress("FunctionName")
-public inline fun <C, A: Ring<C>> A.LabeledPolynomial(capacity: Int, block: LabeledPolynomialBuilder<C>.() -> Unit) : LabeledPolynomial<C> = LabeledPolynomialBuilder(zero, ::add, capacity).apply(block).build()
-@UnstableKMathAPI
-@LabeledPolynomialConstructorDSL
-@Suppress("FunctionName")
-public inline fun <C, A: Ring<C>> LabeledPolynomialSpace<C, A>.LabeledPolynomial(block: LabeledPolynomialBuilder<C>.() -> Unit) : LabeledPolynomial<C> = LabeledPolynomialBuilder(constantZero, { left: C, right: C -> left + right}).apply(block).build()
-@UnstableKMathAPI
-@LabeledPolynomialConstructorDSL
-@Suppress("FunctionName")
-public inline fun <C, A: Ring<C>> LabeledPolynomialSpace<C, A>.LabeledPolynomial(capacity: Int, block: LabeledPolynomialBuilder<C>.() -> Unit) : LabeledPolynomial<C> = LabeledPolynomialBuilder(constantZero, { left: C, right: C -> left + right}, capacity).apply(block).build()
+public inline fun <C, A: Ring<C>> LabeledRationalFunctionSpace<C, A>.LabeledPolynomial(initialCapacity: Int = 0, block: LabeledPolynomialBuilder<C>.() -> Unit) : LabeledPolynomial<C> = LabeledPolynomialBuilder({ left: C, right: C -> left + right }, initialCapacity).apply(block).build()
 
 // Waiting for context receivers :( FIXME: Replace with context receivers when they will be available
 
-@Suppress("FunctionName")
-public fun <C, A: Ring<C>> LabeledRationalFunctionSpace<C, A>.LabeledRationalFunction(numeratorCoefficients: Map<Map<Symbol, UInt>, C>, denominatorCoefficients: Map<Map<Symbol, UInt>, C>): LabeledRationalFunction<C> =
-    LabeledRationalFunction<C>(
-        LabeledPolynomial(numeratorCoefficients, toCheckInput = true),
-        LabeledPolynomial(denominatorCoefficients, toCheckInput = true)
-    )
-@Suppress("FunctionName")
+/**
+ * Constructs [LabeledRationalFunction] with provided coefficients maps [numeratorCoefficients] and [denominatorCoefficients].
+ *
+ * The maps will be "cleaned up":
+ * 1. Zeros at the ends of terms' signatures (e.g. the maps' keys) will be removed. (See [cleanUp].)
+ * 1. Terms that happen to have the same signature will be summed up.
+ * 1. New map will be formed of resulting terms.
+ */
 public fun <C, A: Ring<C>> A.LabeledRationalFunction(numeratorCoefficients: Map<Map<Symbol, UInt>, C>, denominatorCoefficients: Map<Map<Symbol, UInt>, C>): LabeledRationalFunction<C> =
     LabeledRationalFunction<C>(
-        LabeledPolynomial(numeratorCoefficients, toCheckInput = true),
-        LabeledPolynomial(denominatorCoefficients, toCheckInput = true)
+        LabeledPolynomial(numeratorCoefficients),
+        LabeledPolynomial(denominatorCoefficients)
     )
-@Suppress("FunctionName")
+/**
+ * Constructs [LabeledRationalFunction] with provided coefficients maps [numeratorCoefficients] and [denominatorCoefficients].
+ *
+ * The maps will be "cleaned up":
+ * 1. Zeros at the ends of terms' signatures (e.g. the maps' keys) will be removed. (See [cleanUp].)
+ * 1. Terms that happen to have the same signature will be summed up.
+ * 1. New map will be formed of resulting terms.
+ */
+public fun <C, A: Ring<C>> LabeledRationalFunctionSpace<C, A>.LabeledRationalFunction(numeratorCoefficients: Map<Map<Symbol, UInt>, C>, denominatorCoefficients: Map<Map<Symbol, UInt>, C>): LabeledRationalFunction<C> =
+    LabeledRationalFunction<C>(
+        LabeledPolynomial(numeratorCoefficients),
+        LabeledPolynomial(denominatorCoefficients)
+    )
+
+/**
+ * Constructs [LabeledRationalFunction] with provided [numerator] and unit denominator.
+ */
+public fun <C, A: Ring<C>> A.LabeledRationalFunction(numerator: LabeledPolynomial<C>): LabeledRationalFunction<C> =
+    LabeledRationalFunction<C>(numerator, LabeledPolynomial(mapOf(emptyMap<Symbol, UInt>() to one)))
+/**
+ * Constructs [LabeledRationalFunction] with provided [numerator] and unit denominator.
+ */
 public fun <C, A: Ring<C>> LabeledRationalFunctionSpace<C, A>.LabeledRationalFunction(numerator: LabeledPolynomial<C>): LabeledRationalFunction<C> =
     LabeledRationalFunction<C>(numerator, polynomialOne)
-@Suppress("FunctionName")
-public fun <C, A: Ring<C>> A.LabeledRationalFunction(numerator: LabeledPolynomial<C>): LabeledRationalFunction<C> =
-    LabeledRationalFunction<C>(numerator, LabeledPolynomial(mapOf(emptyMap<Symbol, UInt>() to one), toCheckInput = false))
-@Suppress("FunctionName")
+
+/**
+ * Constructs [LabeledRationalFunction] with provided coefficients map [numeratorCoefficients] for numerator and unit
+ * denominator.
+ *
+ * [numeratorCoefficients] will be "cleaned up":
+ * 1. Zeros at the ends of terms' signatures (e.g. [numeratorCoefficients]'s keys) will be removed. (See [cleanUp].)
+ * 1. Terms that happen to have the same signature will be summed up.
+ * 1. New map will be formed of resulting terms.
+ */
 public fun <C, A: Ring<C>> LabeledRationalFunctionSpace<C, A>.LabeledRationalFunction(numeratorCoefficients: Map<Map<Symbol, UInt>, C>): LabeledRationalFunction<C> =
     LabeledRationalFunction<C>(
-        LabeledPolynomial(numeratorCoefficients, toCheckInput = true),
+        LabeledPolynomial(numeratorCoefficients),
         polynomialOne
     )
-@Suppress("FunctionName")
+/**
+ * Constructs [LabeledRationalFunction] with provided coefficients map [numeratorCoefficients] for numerator and unit
+ * denominator.
+ *
+ * [numeratorCoefficients] will be "cleaned up":
+ * 1. Zeros at the ends of terms' signatures (e.g. [numeratorCoefficients]'s keys) will be removed. (See [cleanUp].)
+ * 1. Terms that happen to have the same signature will be summed up.
+ * 1. New map will be formed of resulting terms.
+ */
 public fun <C, A: Ring<C>> A.LabeledRationalFunction(numeratorCoefficients: Map<Map<Symbol, UInt>, C>): LabeledRationalFunction<C> =
     LabeledRationalFunction<C>(
-        LabeledPolynomial(numeratorCoefficients, toCheckInput = true),
-        LabeledPolynomial(mapOf(emptyMap<Symbol, UInt>() to one), toCheckInput = false)
+        LabeledPolynomial(numeratorCoefficients),
+        LabeledPolynomialAsIs(mapOf(emptyMap<Symbol, UInt>() to one))
     )
 
+///**
+// * Converts [this] constant to [LabeledRationalFunction].
+// */
 //context(A)
-//public fun <C, A: Ring<C>> Symbol.asLabeledRationalFunction() : LabeledRationalFunction<C> = LabeledRationalFunction(asLabeledPolynomial())
+//public fun <C, A: Ring<C>> C.asLabeledRationalFunction() : LabeledRationalFunction<C> =
+//    LabeledRationalFunction(
+//        LabeledPolynomialAsIs(mapOf(emptyMap<Symbol, UInt>() to this)),
+//        LabeledPolynomialAsIs(mapOf(emptyMap<Symbol, UInt>() to one))
+//    )
+///**
+// * Converts [this] constant to [LabeledRationalFunction].
+// */
 //context(LabeledRationalFunctionSpace<C, A>)
-//public fun <C, A: Ring<C>> Symbol.asLabeledRationalFunction() : LabeledRationalFunction<C> = LabeledRationalFunction(asLabeledPolynomial())
+//public fun <C, A: Ring<C>> C.asLabeledRationalFunction() : LabeledRationalFunction<C> =
+//    LabeledRationalFunction(
+//        LabeledPolynomialAsIs(mapOf(emptyMap<Symbol, UInt>() to this)),
+//        LabeledPolynomialAsIs(mapOf(emptyMap<Symbol, UInt>() to constantOne))
+//    )
 
+///**
+// * Converts [this] variable to [LabeledRationalFunction].
+// */
 //context(A)
-//public fun <C, A: Ring<C>> C.asLabeledRationalFunction() : LabeledRationalFunction<C> = LabeledRationalFunction(asLabeledPolynomial())
+//public fun <C, A: Ring<C>> Symbol.asLabeledRationalFunction() : LabeledRationalFunction<C> =
+//    LabeledRationalFunction(
+//        LabeledPolynomialAsIs(mapOf(mapOf(this to 1u) to one)),
+//        LabeledPolynomialAsIs(mapOf(emptyMap<Symbol, UInt>() to one))
+//    )
+///**
+// * Converts [this] variable to [LabeledRationalFunction].
+// */
 //context(LabeledRationalFunctionSpace<C, A>)
-//public fun <C, A: Ring<C>> C.asLabeledRationalFunction() : LabeledRationalFunction<C> = LabeledRationalFunction(asLabeledPolynomial())
+//public fun <C, A: Ring<C>> Symbol.asLabeledRationalFunction() : LabeledRationalFunction<C> =
+//    LabeledRationalFunction(
+//        LabeledPolynomialAsIs(mapOf(mapOf(this to 1u) to constantOne)),
+//        LabeledPolynomialAsIs(mapOf(emptyMap<Symbol, UInt>() to constantOne))
+//    )

kmath-functions/src/commonMain/kotlin/space/kscience/kmath/functions/labeledPolynomialUtil.kt

@@ -1,495 +0,0 @@
-/*
- * Copyright 2018-2021 KMath contributors.
- * Use of this source code is governed by the Apache 2.0 license that can be found in the license/LICENSE.txt file.
- */
-
-package space.kscience.kmath.functions
-
-import space.kscience.kmath.expressions.Symbol
-import space.kscience.kmath.misc.UnstableKMathAPI
-import space.kscience.kmath.operations.Field
-import space.kscience.kmath.operations.Ring
-import space.kscience.kmath.operations.invoke
-import kotlin.contracts.ExperimentalContracts
-import kotlin.contracts.InvocationKind
-import kotlin.contracts.contract
-
-
-// TODO: Docs
-
-/**
- * Creates a [LabeledPolynomialSpace] over a received ring.
- */
-public fun <C, A : Ring<C>> A.labeledPolynomial(): LabeledPolynomialSpace<C, A> =
-    LabeledPolynomialSpace(this)
-
-/**
- * Creates a [LabeledPolynomialSpace]'s scope over a received ring.
- */
-@OptIn(ExperimentalContracts::class)
-public inline fun <C, A : Ring<C>, R> A.labeledPolynomial(block: LabeledPolynomialSpace<C, A>.() -> R): R {
-    contract { callsInPlace(block, InvocationKind.EXACTLY_ONCE) }
-    return LabeledPolynomialSpace(this).block()
-}
-
-///**
-// * Represents the polynomial as a [String] with names of variables substituted with names from [names].
-// * Consider that monomials are sorted in lexicographic order.
-// */
-//context(LabeledPolynomialSpace<C, A>)
-//fun <C, A: Ring<C>> LabeledPolynomial<C>.represent(names: Map<Symbol, String> = emptyMap()): String =
-//    coefficients.entries
-//        .sortedWith { o1, o2 -> LabeledPolynomial.monomialComparator.compare(o1.key, o2.key) }
-//        .asSequence()
-//        .map { (degs, t) ->
-//            if (degs.isEmpty()) "$t"
-//            else {
-//                when {
-//                    t.isOne() -> ""
-//                    t.isMinusOne() -> "-"
-//                    else -> "$t "
-//                } +
-//                        degs
-//                            .toSortedMap()
-//                            .filter { it.value > 0U }
-//                            .map { (variable, deg) ->
-//                                val variableName = names.getOrDefault(variable, variable.toString())
-//                                when (deg) {
-//                                    1U -> variableName
-//                                    else -> "$variableName^$deg"
-//                                }
-//                            }
-//                            .joinToString(separator = " ") { it }
-//            }
-//        }
-//        .joinToString(separator = " + ") { it }
-//        .ifEmpty { "0" }
-//
-///**
-// * Represents the polynomial as a [String] naming variables by [namer].
-// * Consider that monomials are sorted in lexicographic order.
-// */
-//context(LabeledPolynomialSpace<C, A>)
-//fun <C, A: Ring<C>> LabeledPolynomial<C>.represent(namer: (Symbol) -> String): String =
-//    coefficients.entries
-//        .sortedWith { o1, o2 -> LabeledPolynomial.monomialComparator.compare(o1.key, o2.key) }
-//        .asSequence()
-//        .map { (degs, t) ->
-//            if (degs.isEmpty()) "$t"
-//            else {
-//                when {
-//                    t.isOne() -> ""
-//                    t.isMinusOne() -> "-"
-//                    else -> "$t "
-//                } +
-//                        degs
-//                            .toSortedMap()
-//                            .filter { it.value > 0U }
-//                            .map { (variable, deg) ->
-//                                when (deg) {
-//                                    1U -> namer(variable)
-//                                    else -> "${namer(variable)}^$deg"
-//                                }
-//                            }
-//                            .joinToString(separator = " ") { it }
-//            }
-//        }
-//        .joinToString(separator = " + ") { it }
-//        .ifEmpty { "0" }
-//
-///**
-// * Represents the polynomial as a [String] with names of variables substituted with names from [names] and with
-// * brackets around the string if needed (i.e. when there are at least two addends in the representation).
-// * Consider that monomials are sorted in lexicographic order.
-// */
-//context(LabeledPolynomialSpace<C, A>)
-//fun <C, A: Ring<C>> LabeledPolynomial<C>.representWithBrackets(names: Map<Symbol, String> = emptyMap()): String =
-//    with(represent(names)) { if (coefficients.count() == 1) this else "($this)" }
-//
-///**
-// * Represents the polynomial as a [String] naming variables by [namer] and with brackets around the string if needed
-// * (i.e. when there are at least two addends in the representation).
-// * Consider that monomials are sorted in lexicographic order.
-// */
-//context(LabeledPolynomialSpace<C, A>)
-//fun <C, A: Ring<C>> LabeledPolynomial<C>.representWithBrackets(namer: (Symbol) -> String): String =
-//    with(represent(namer)) { if (coefficients.count() == 1) this else "($this)" }
-//
-///**
-// * Represents the polynomial as a [String] with names of variables substituted with names from [names].
-// * Consider that monomials are sorted in **reversed** lexicographic order.
-// */
-//context(LabeledPolynomialSpace<C, A>)
-//fun <C, A: Ring<C>> LabeledPolynomial<C>.representReversed(names: Map<Symbol, String> = emptyMap()): String =
-//    coefficients.entries
-//        .sortedWith { o1, o2 -> -LabeledPolynomial.monomialComparator.compare(o1.key, o2.key) }
-//        .asSequence()
-//        .map { (degs, t) ->
-//            if (degs.isEmpty()) "$t"
-//            else {
-//                when {
-//                    t.isOne() -> ""
-//                    t.isMinusOne() -> "-"
-//                    else -> "$t "
-//                } +
-//                        degs
-//                            .toSortedMap()
-//                            .filter { it.value > 0U }
-//                            .map { (variable, deg) ->
-//                                val variableName = names.getOrDefault(variable, variable.toString())
-//                                when (deg) {
-//                                    1U -> variableName
-//                                    else -> "$variableName^$deg"
-//                                }
-//                            }
-//                            .joinToString(separator = " ") { it }
-//            }
-//        }
-//        .joinToString(separator = " + ") { it }
-//        .ifEmpty { "0" }
-//
-///**
-// * Represents the polynomial as a [String] naming variables by [namer].
-// * Consider that monomials are sorted in **reversed** lexicographic order.
-// */
-//context(LabeledPolynomialSpace<C, A>)
-//fun <C, A: Ring<C>> LabeledPolynomial<C>.representReversed(namer: (Symbol) -> String): String =
-//    coefficients.entries
-//        .sortedWith { o1, o2 -> -LabeledPolynomial.monomialComparator.compare(o1.key, o2.key) }
-//        .asSequence()
-//        .map { (degs, t) ->
-//            if (degs.isEmpty()) "$t"
-//            else {
-//                when {
-//                    t.isOne() -> ""
-//                    t.isMinusOne() -> "-"
-//                    else -> "$t "
-//                } +
-//                        degs
-//                            .toSortedMap()
-//                            .filter { it.value > 0U }
-//                            .map { (variable, deg) ->
-//                                when (deg) {
-//                                    1U -> namer(variable)
-//                                    else -> "${namer(variable)}^$deg"
-//                                }
-//                            }
-//                            .joinToString(separator = " ") { it }
-//            }
-//        }
-//        .joinToString(separator = " + ") { it }
-//        .ifEmpty { "0" }
-//
-///**
-// * Represents the polynomial as a [String] with names of variables substituted with names from [names] and with
-// * brackets around the string if needed (i.e. when there are at least two addends in the representation).
-// * Consider that monomials are sorted in **reversed** lexicographic order.
-// */
-//context(LabeledPolynomialSpace<C, A>)
-//fun <C, A: Ring<C>> LabeledPolynomial<C>.representReversedWithBrackets(names: Map<Symbol, String> = emptyMap()): String =
-//    with(representReversed(names)) { if (coefficients.count() == 1) this else "($this)" }
-//
-///**
-// * Represents the polynomial as a [String] naming variables by [namer] and with brackets around the string if needed
-// * (i.e. when there are at least two addends in the representation).
-// * Consider that monomials are sorted in **reversed** lexicographic order.
-// */
-//context(LabeledPolynomialSpace<C, A>)
-//fun <C, A: Ring<C>> LabeledPolynomial<C>.representReversedWithBrackets(namer: (Symbol) -> String): String =
-//    with(representReversed(namer)) { if (coefficients.count() == 1) this else "($this)" }
-
-//operator fun <T: Field<T>> Polynomial<T>.div(other: T): Polynomial<T> =
-//    if (other.isZero()) throw ArithmeticException("/ by zero")
-//    else
-//        Polynomial(
-//            coefficients
-//                .mapValues { it.value / other },
-//            toCheckInput = false
-//        )
-
-//public fun <C> LabeledPolynomial<C>.substitute(ring: Ring<C>, args: Map<Symbol, C>): LabeledPolynomial<C> = ring {
-//    if (coefficients.isEmpty()) return this@substitute
-//    LabeledPolynomial<C>(
-//        buildMap {
-//            coefficients.forEach { (degs, c) ->
-//                val newDegs = degs.filterKeys { it !in args }
-//                val newC = degs.entries.asSequence().filter { it.key in args }.fold(c) { acc, (variable, deg) ->
-//                    multiplyWithPower(acc, args[variable]!!, deg)
-//                }
-//                this[newDegs] = if (newDegs in this) this[newDegs]!! + newC else newC
-//            }
-//        }
-//    )
-//}
-//
-//// TODO: Replace with optimisation: the [result] may be unboxed, and all operations may be performed as soon as
-////  possible on it
-//@JvmName("substitutePolynomial")
-//fun <C> LabeledPolynomial<C>.substitute(ring: Ring<C>, arg: Map<Symbol, LabeledPolynomial<C>>) : LabeledPolynomial<C> =
-//    ring.labeledPolynomial {
-//        if (coefficients.isEmpty()) return zero
-//        coefficients
-//            .asSequence()
-//            .map { (degs, c) ->
-//                degs.entries
-//                    .asSequence()
-//                    .filter { it.key in arg }
-//                    .fold(LabeledPolynomial(mapOf(degs.filterKeys { it !in arg } to c))) { acc, (index, deg) ->
-//                        multiplyWithPower(acc, arg[index]!!, deg)
-//                    }
-//            }
-//            .reduce { acc, polynomial -> acc + polynomial } // TODO: Rewrite. Might be slow.
-//    }
-//
-//// TODO: Substitute rational function
-//
-//fun <C, A : Ring<C>> LabeledPolynomial<C>.asFunctionOver(ring: A): (Map<Symbol, C>) -> LabeledPolynomial<C> =
-//    { substitute(ring, it) }
-//
-//fun <C, A : Ring<C>> LabeledPolynomial<C>.asPolynomialFunctionOver(ring: A): (Map<Symbol, LabeledPolynomial<C>>) -> LabeledPolynomial<C> =
-//    { substitute(ring, it) }
-
-/**
- * Returns algebraic derivative of received polynomial.
- */
-@UnstableKMathAPI
-public fun <C, A : Ring<C>> LabeledPolynomial<C>.derivativeWithRespectTo(
-    algebra: A,
-    variable: Symbol,
-): LabeledPolynomial<C> = algebra {
-    LabeledPolynomial<C>(
-        buildMap(coefficients.size) {
-            coefficients
-                .forEach { (degs, c) ->
-                    if (variable !in degs) return@forEach
-                    put(
-                        buildMap {
-                            degs.forEach { (vari, deg) ->
-                                when {
-                                    vari != variable -> put(vari, deg)
-                                    deg > 1u -> put(vari, deg - 1u)
-                                }
-                            }
-                        },
-                        multiplyByDoubling(c, degs[variable]!!)
-                    )
-                }
-        }
-    )
-}
-
-/**
- * Returns algebraic derivative of received polynomial.
- */
-@UnstableKMathAPI
-public fun <C, A : Ring<C>> LabeledPolynomial<C>.derivativeWithRespectTo(
-    algebra: A,
-    variables: Collection<Symbol>,
-): LabeledPolynomial<C> = algebra {
-    val cleanedVariables = variables.toSet()
-    if (cleanedVariables.isEmpty()) return this@derivativeWithRespectTo
-    LabeledPolynomial<C>(
-        buildMap(coefficients.size) {
-            coefficients
-                .forEach { (degs, c) ->
-                    if (!degs.keys.containsAll(cleanedVariables)) return@forEach
-                    put(
-                        buildMap {
-                            degs.forEach { (vari, deg) ->
-                                when {
-                                    vari !in cleanedVariables -> put(vari, deg)
-                                    deg > 1u -> put(vari, deg - 1u)
-                                }
-                            }
-                        },
-                        cleanedVariables.fold(c) { acc, variable -> multiplyByDoubling(acc, degs[variable]!!) }
-                    )
-                }
-        }
-    )
-}
-
-/**
- * Returns algebraic derivative of received polynomial.
- */
-@UnstableKMathAPI
-public fun <C, A : Ring<C>> LabeledPolynomial<C>.nthDerivativeWithRespectTo(
-    algebra: A,
-    variable: Symbol,
-    order: UInt
-): LabeledPolynomial<C> = algebra {
-    if (order == 0u) return this@nthDerivativeWithRespectTo
-    LabeledPolynomial<C>(
-        buildMap(coefficients.size) {
-            coefficients
-                .forEach { (degs, c) ->
-                    if (degs.getOrElse(variable) { 0u } < order) return@forEach
-                    put(
-                        buildMap {
-                            degs.forEach { (vari, deg) ->
-                                when {
-                                    vari != variable -> put(vari, deg)
-                                    deg > order -> put(vari, deg - order)
-                                }
-                            }
-                        },
-                        degs[variable]!!.let { deg ->
-                            (deg downTo deg - order + 1u)
-                                .fold(c) { acc, ord -> multiplyByDoubling(acc, ord) }
-                        }
-                    )
-                }
-        }
-    )
-}
-
-/**
- * Returns algebraic derivative of received polynomial.
- */
-@UnstableKMathAPI
-public fun <C, A : Ring<C>> LabeledPolynomial<C>.nthDerivativeWithRespectTo(
-    algebra: A,
-    variablesAndOrders: Map<Symbol, UInt>,
-): LabeledPolynomial<C> = algebra {
-    val filteredVariablesAndOrders = variablesAndOrders.filterValues { it != 0u }
-    if (filteredVariablesAndOrders.isEmpty()) return this@nthDerivativeWithRespectTo
-    LabeledPolynomial<C>(
-        buildMap(coefficients.size) {
-            coefficients
-                .forEach { (degs, c) ->
-                    if (filteredVariablesAndOrders.any { (variable, order) -> degs.getOrElse(variable) { 0u } < order }) return@forEach
-                    put(
-                        buildMap {
-                            degs.forEach { (vari, deg) ->
-                                if (vari !in filteredVariablesAndOrders) put(vari, deg)
-                                else {
-                                    val order = filteredVariablesAndOrders[vari]!!
-                                    if (deg > order) put(vari, deg - order)
-                                }
-                            }
-                        },
-                        filteredVariablesAndOrders.entries.fold(c) { acc1, (index, order) ->
-                            degs[index]!!.let { deg ->
-                                (deg downTo deg - order + 1u)
-                                    .fold(acc1) { acc2, ord -> multiplyByDoubling(acc2, ord) }
-                            }
-                        }
-                    )
-                }
-        }
-    )
-}
-
-/**
- * Returns algebraic antiderivative of received polynomial.
- */
-@UnstableKMathAPI
-public fun <C, A : Field<C>> LabeledPolynomial<C>.antiderivativeWithRespectTo(
-    algebra: A,
-    variable: Symbol,
-): LabeledPolynomial<C> = algebra {
-    LabeledPolynomial<C>(
-        buildMap(coefficients.size) {
-            coefficients
-                .forEach { (degs, c) ->
-                    val newDegs = buildMap<Symbol, UInt>(degs.size + 1) {
-                        put(variable, 1u)
-                        for ((vari, deg) in degs) put(vari, deg + getOrElse(vari) { 0u })
-                    }
-                    put(
-                        newDegs,
-                        c / multiplyByDoubling(one, newDegs[variable]!!)
-                    )
-                }
-        }
-    )
-}
-
-/**
- * Returns algebraic antiderivative of received polynomial.
- */
-@UnstableKMathAPI
-public fun <C, A : Field<C>> LabeledPolynomial<C>.antiderivativeWithRespectTo(
-    algebra: A,
-    variables: Collection<Symbol>,
-): LabeledPolynomial<C> = algebra {
-    val cleanedVariables = variables.toSet()
-    if (cleanedVariables.isEmpty()) return this@antiderivativeWithRespectTo
-    LabeledPolynomial<C>(
-        buildMap(coefficients.size) {
-            coefficients
-                .forEach { (degs, c) ->
-                    val newDegs = buildMap<Symbol, UInt>(degs.size + 1) {
-                        for (variable in cleanedVariables) put(variable, 1u)
-                        for ((vari, deg) in degs) put(vari, deg + getOrElse(vari) { 0u })
-                    }
-                    put(
-                        newDegs,
-                        cleanedVariables.fold(c) { acc, variable -> acc / multiplyByDoubling(one, newDegs[variable]!!) }
-                    )
-                }
-        }
-    )
-}
-
-/**
- * Returns algebraic derivative of received polynomial.
- */
-@UnstableKMathAPI
-public fun <C, A : Field<C>> LabeledPolynomial<C>.nthAntiderivativeWithRespectTo(
-    algebra: A,
-    variable: Symbol,
-    order: UInt
-): LabeledPolynomial<C> = algebra {
-    if (order == 0u) return this@nthAntiderivativeWithRespectTo
-    LabeledPolynomial<C>(
-        buildMap(coefficients.size) {
-            coefficients
-                .forEach { (degs, c) ->
-                    val newDegs = buildMap<Symbol, UInt>(degs.size + 1) {
-                        put(variable, order)
-                        for ((vari, deg) in degs) put(vari, deg + getOrElse(vari) { 0u })
-                    }
-                    put(
-                        newDegs,
-                        newDegs[variable]!!.let { deg ->
-                            (deg downTo  deg - order + 1u)
-                                .fold(c) { acc, ord -> acc / multiplyByDoubling(one, ord) }
-                        }
-                    )
-                }
-        }
-    )
-}
-
-/**
- * Returns algebraic derivative of received polynomial.
- */
-@UnstableKMathAPI
-public fun <C, A : Field<C>> LabeledPolynomial<C>.nthAntiderivativeWithRespectTo(
-    algebra: A,
-    variablesAndOrders: Map<Symbol, UInt>,
-): LabeledPolynomial<C> = algebra {
-    val filteredVariablesAndOrders = variablesAndOrders.filterValues { it != 0u }
-    if (filteredVariablesAndOrders.isEmpty()) return this@nthAntiderivativeWithRespectTo
-    LabeledPolynomial<C>(
-        buildMap(coefficients.size) {
-            coefficients
-                .forEach { (degs, c) ->
-                    val newDegs = buildMap<Symbol, UInt>(degs.size + 1) {
-                        for ((variable, order) in filteredVariablesAndOrders) put(variable, order)
-                        for ((vari, deg) in degs) put(vari, deg + getOrElse(vari) { 0u })
-                    }
-                    put(
-                        newDegs,
-                        filteredVariablesAndOrders.entries.fold(c) { acc1, (index, order) ->
-                            newDegs[index]!!.let { deg ->
-                                (deg downTo deg - order + 1u)
-                                    .fold(acc1) { acc2, ord -> acc2 / multiplyByDoubling(one, ord) }
-                            }
-                        }
-                    )
-                }
-        }
-    )
-}

kmath-functions/src/commonMain/kotlin/space/kscience/kmath/functions/labeledRationalFunctionUtil.kt

@@ -1,33 +0,0 @@
-/*
- * Copyright 2018-2021 KMath contributors.
- * Use of this source code is governed by the Apache 2.0 license that can be found in the license/LICENSE.txt file.
- */
-
-package space.kscience.kmath.functions
-
-import space.kscience.kmath.operations.Ring
-import kotlin.contracts.InvocationKind
-import kotlin.contracts.contract
-
-
-/**
- * Creates a [LabeledRationalFunctionSpace] over a received ring.
- */
-public fun <C, A : Ring<C>> A.labeledRationalFunction(): LabeledRationalFunctionSpace<C, A> =
-    LabeledRationalFunctionSpace(this)
-
-/**
- * Creates a [LabeledRationalFunctionSpace]'s scope over a received ring.
- */
-public inline fun <C, A : Ring<C>, R> A.labeledRationalFunction(block: LabeledRationalFunctionSpace<C, A>.() -> R): R {
-    contract { callsInPlace(block, InvocationKind.EXACTLY_ONCE) }
-    return LabeledRationalFunctionSpace(this).block()
-}
-
-//fun <T: Field<T>> LabeledRationalFunction<T>.reduced(): LabeledRationalFunction<T> {
-//    val greatestCommonDivider = polynomialGCD(numerator, denominator)
-//    return LabeledRationalFunction(
-//        numerator / greatestCommonDivider,
-//        denominator / greatestCommonDivider
-//    )
-//}

kmath-functions/src/commonMain/kotlin/space/kscience/kmath/functions/labeledUtil.kt

@@ -0,0 +1,327 @@
+/*
+ * Copyright 2018-2021 KMath contributors.
+ * Use of this source code is governed by the Apache 2.0 license that can be found in the license/LICENSE.txt file.
+ */
+
+package space.kscience.kmath.functions
+
+import space.kscience.kmath.expressions.Symbol
+import space.kscience.kmath.misc.UnstableKMathAPI
+import space.kscience.kmath.operations.Field
+import space.kscience.kmath.operations.invoke
+import space.kscience.kmath.operations.Ring
+import space.kscience.kmath.operations.algebra
+import kotlin.contracts.InvocationKind
+import kotlin.contracts.contract
+import kotlin.jvm.JvmName
+
+
+/**
+ * Creates a [LabeledPolynomialSpace] over a received ring.
+ */
+public fun <C, A : Ring<C>> A.labeledPolynomialSpace(): LabeledPolynomialSpace<C, A> =
+    LabeledPolynomialSpace(this)
+
+/**
+ * Creates a [LabeledPolynomialSpace]'s scope over a received ring.
+ */
+public inline fun <C, A : Ring<C>, R> A.labeledPolynomialSpace(block: LabeledPolynomialSpace<C, A>.() -> R): R {
+    contract { callsInPlace(block, InvocationKind.EXACTLY_ONCE) }
+    return LabeledPolynomialSpace(this).block()
+}
+/**
+ * Creates a [LabeledRationalFunctionSpace] over a received ring.
+ */
+public fun <C, A : Ring<C>> A.labeledRationalFunctionSpace(): LabeledRationalFunctionSpace<C, A> =
+    LabeledRationalFunctionSpace(this)
+
+/**
+ * Creates a [LabeledRationalFunctionSpace]'s scope over a received ring.
+ */
+public inline fun <C, A : Ring<C>, R> A.labeledRationalFunctionSpace(block: LabeledRationalFunctionSpace<C, A>.() -> R): R {
+    contract { callsInPlace(block, InvocationKind.EXACTLY_ONCE) }
+    return LabeledRationalFunctionSpace(this).block()
+}
+
+/**
+ * Substitutes provided Double arguments [args] into [this] Double polynomial.
+ */
+public fun LabeledPolynomial<Double>.substitute(args: Map<Symbol, Double>): LabeledPolynomial<Double> = Double.algebra {
+    if (coefficients.isEmpty()) return this@substitute
+    LabeledPolynomial<Double>(
+        buildMap {
+            coefficients.forEach { (degs, c) ->
+                val newDegs = degs.filterKeys { it !in args }
+                val newC = args.entries.fold(c) { product, (variable, substitution) ->
+                    val deg = degs.getOrElse(variable) { 0u }
+                    if (deg == 0u) product else product * power(substitution, deg)
+                }
+                this[newDegs] = if (newDegs in this) this[newDegs]!! + newC else newC
+            }
+        }
+    )
+}
+
+/**
+ * Substitutes provided arguments [args] into [this] polynomial.
+ */
+public fun <C> LabeledPolynomial<C>.substitute(ring: Ring<C>, args: Map<Symbol, C>): LabeledPolynomial<C> = ring {
+    if (coefficients.isEmpty()) return this@substitute
+    LabeledPolynomial<C>(
+        buildMap {
+            coefficients.forEach { (degs, c) ->
+                val newDegs = degs.filterKeys { it !in args }
+                val newC = args.entries.fold(c) { product, (variable, substitution) ->
+                    val deg = degs.getOrElse(variable) { 0u }
+                    if (deg == 0u) product else product * power(substitution, deg)
+                }
+                this[newDegs] = if (newDegs in this) this[newDegs]!! + newC else newC
+            }
+        }
+    )
+}
+
+/**
+ * Substitutes provided arguments [args] into [this] polynomial.
+ */ // TODO: To optimize boxing
+@JvmName("substitutePolynomial")
+public fun <C> LabeledPolynomial<C>.substitute(ring: Ring<C>, args: Map<Symbol, LabeledPolynomial<C>>) : LabeledPolynomial<C> =
+    ring.labeledPolynomialSpace {
+        coefficients.entries.fold(zero) { acc, (degs, c) ->
+            val newDegs = degs.filterKeys { it !in args }
+            acc + args.entries.fold(LabeledPolynomial<C>(mapOf(newDegs to c))) { product, (variable, substitution) ->
+                val deg = degs.getOrElse(variable) { 0u }
+                if (deg == 0u) product else product * power(substitution, deg)
+            }
+        }
+    }
+
+/**
+ * Substitutes provided arguments [args] into [this] polynomial.
+ */ // TODO: To optimize boxing
+@JvmName("substituteRationalFunction")
+public fun <C> LabeledPolynomial<C>.substitute(ring: Ring<C>, args: Map<Symbol, LabeledRationalFunction<C>>) : LabeledRationalFunction<C> =
+    ring.labeledRationalFunctionSpace {
+        coefficients.entries.fold(zero) { acc, (degs, c) ->
+            val newDegs = degs.filterKeys { it !in args }
+            acc + args.entries.fold(LabeledRationalFunction(LabeledPolynomial<C>(mapOf(newDegs to c)))) { product, (variable, substitution) ->
+                val deg = degs.getOrElse(variable) { 0u }
+                if (deg == 0u) product else product * power(substitution, deg)
+            }
+        }
+    }
+
+/**
+ * Substitutes provided Double arguments [args] into [this] Double rational function.
+ */
+public fun LabeledRationalFunction<Double>.substitute(args: Map<Symbol, Double>): LabeledRationalFunction<Double> =
+    LabeledRationalFunction(numerator.substitute(args), denominator.substitute(args))
+
+/**
+ * Substitutes provided arguments [args] into [this] rational function.
+ */
+public fun <C> LabeledRationalFunction<C>.substitute(ring: Ring<C>, args: Map<Symbol, C>): LabeledRationalFunction<C> =
+    LabeledRationalFunction(numerator.substitute(ring, args), denominator.substitute(ring, args))
+
+/**
+ * Substitutes provided arguments [args] into [this] rational function.
+ */ // TODO: To optimize calculation
+@JvmName("substitutePolynomial")
+public fun <C> LabeledRationalFunction<C>.substitute(ring: Ring<C>, args: Map<Symbol, LabeledPolynomial<C>>) : LabeledRationalFunction<C> =
+    LabeledRationalFunction(numerator.substitute(ring, args), denominator.substitute(ring, args))
+
+/**
+ * Substitutes provided arguments [args] into [this] rational function.
+ */ // TODO: To optimize calculation
+@JvmName("substituteRationalFunction")
+public fun <C> LabeledRationalFunction<C>.substitute(ring: Ring<C>, args: Map<Symbol, LabeledRationalFunction<C>>) : LabeledRationalFunction<C> =
+    ring.labeledRationalFunctionSpace {
+        numerator.substitute(ring, args) / denominator.substitute(ring, args)
+    }
+
+/**
+ * Returns algebraic derivative of received polynomial with respect to provided variable.
+ */
+@UnstableKMathAPI
+public fun <C, A : Ring<C>> LabeledPolynomial<C>.derivativeWithRespectTo(
+    algebra: A,
+    variable: Symbol,
+): LabeledPolynomial<C> = algebra {
+    LabeledPolynomial<C>(
+        buildMap(coefficients.size) {
+            coefficients
+                .forEach { (degs, c) ->
+                    if (variable !in degs) return@forEach
+                    put(
+                        buildMap {
+                            degs.forEach { (vari, deg) ->
+                                when {
+                                    vari != variable -> put(vari, deg)
+                                    deg > 1u -> put(vari, deg - 1u)
+                                }
+                            }
+                        },
+                        multiplyByDoubling(c, degs[variable]!!)
+                    )
+                }
+        }
+    )
+}
+
+/**
+ * Returns algebraic derivative of received polynomial with respect to provided variable of specified order.
+ */
+@UnstableKMathAPI
+public fun <C, A : Ring<C>> LabeledPolynomial<C>.nthDerivativeWithRespectTo(
+    algebra: A,
+    variable: Symbol,
+    order: UInt
+): LabeledPolynomial<C> = algebra {
+    if (order == 0u) return this@nthDerivativeWithRespectTo
+    LabeledPolynomial<C>(
+        buildMap(coefficients.size) {
+            coefficients
+                .forEach { (degs, c) ->
+                    if (degs.getOrElse(variable) { 0u } < order) return@forEach
+                    put(
+                        buildMap {
+                            degs.forEach { (vari, deg) ->
+                                when {
+                                    vari != variable -> put(vari, deg)
+                                    deg > order -> put(vari, deg - order)
+                                }
+                            }
+                        },
+                        degs[variable]!!.let { deg ->
+                            (deg downTo deg - order + 1u)
+                                .fold(c) { acc, ord -> multiplyByDoubling(acc, ord) }
+                        }
+                    )
+                }
+        }
+    )
+}
+
+/**
+ * Returns algebraic derivative of received polynomial with respect to provided variables of specified orders.
+ */
+@UnstableKMathAPI
+public fun <C, A : Ring<C>> LabeledPolynomial<C>.nthDerivativeWithRespectTo(
+    algebra: A,
+    variablesAndOrders: Map<Symbol, UInt>,
+): LabeledPolynomial<C> = algebra {
+    val filteredVariablesAndOrders = variablesAndOrders.filterValues { it != 0u }
+    if (filteredVariablesAndOrders.isEmpty()) return this@nthDerivativeWithRespectTo
+    LabeledPolynomial<C>(
+        buildMap(coefficients.size) {
+            coefficients
+                .forEach { (degs, c) ->
+                    if (filteredVariablesAndOrders.any { (variable, order) -> degs.getOrElse(variable) { 0u } < order }) return@forEach
+                    put(
+                        buildMap {
+                            degs.forEach { (vari, deg) ->
+                                if (vari !in filteredVariablesAndOrders) put(vari, deg)
+                                else {
+                                    val order = filteredVariablesAndOrders[vari]!!
+                                    if (deg > order) put(vari, deg - order)
+                                }
+                            }
+                        },
+                        filteredVariablesAndOrders.entries.fold(c) { acc1, (index, order) ->
+                            degs[index]!!.let { deg ->
+                                (deg downTo deg - order + 1u)
+                                    .fold(acc1) { acc2, ord -> multiplyByDoubling(acc2, ord) }
+                            }
+                        }
+                    )
+                }
+        }
+    )
+}
+
+/**
+ * Returns algebraic antiderivative of received polynomial with respect to provided variable.
+ */
+@UnstableKMathAPI
+public fun <C, A : Field<C>> LabeledPolynomial<C>.antiderivativeWithRespectTo(
+    algebra: A,
+    variable: Symbol,
+): LabeledPolynomial<C> = algebra {
+    LabeledPolynomial<C>(
+        buildMap(coefficients.size) {
+            coefficients
+                .forEach { (degs, c) ->
+                    val newDegs = buildMap<Symbol, UInt>(degs.size + 1) {
+                        put(variable, 1u)
+                        for ((vari, deg) in degs) put(vari, deg + getOrElse(vari) { 0u })
+                    }
+                    put(
+                        newDegs,
+                        c / multiplyByDoubling(one, newDegs[variable]!!)
+                    )
+                }
+        }
+    )
+}
+
+/**
+ * Returns algebraic antiderivative of received polynomial with respect to provided variable of specified order.
+ */
+@UnstableKMathAPI
+public fun <C, A : Field<C>> LabeledPolynomial<C>.nthAntiderivativeWithRespectTo(
+    algebra: A,
+    variable: Symbol,
+    order: UInt
+): LabeledPolynomial<C> = algebra {
+    if (order == 0u) return this@nthAntiderivativeWithRespectTo
+    LabeledPolynomial<C>(
+        buildMap(coefficients.size) {
+            coefficients
+                .forEach { (degs, c) ->
+                    val newDegs = buildMap<Symbol, UInt>(degs.size + 1) {
+                        put(variable, order)
+                        for ((vari, deg) in degs) put(vari, deg + getOrElse(vari) { 0u })
+                    }
+                    put(
+                        newDegs,
+                        newDegs[variable]!!.let { deg ->
+                            (deg downTo  deg - order + 1u)
+                                .fold(c) { acc, ord -> acc / multiplyByDoubling(one, ord) }
+                        }
+                    )
+                }
+        }
+    )
+}
+
+/**
+ * Returns algebraic derivative of received polynomial with respect to provided variables of specified orders.
+ */
+@UnstableKMathAPI
+public fun <C, A : Field<C>> LabeledPolynomial<C>.nthAntiderivativeWithRespectTo(
+    algebra: A,
+    variablesAndOrders: Map<Symbol, UInt>,
+): LabeledPolynomial<C> = algebra {
+    val filteredVariablesAndOrders = variablesAndOrders.filterValues { it != 0u }
+    if (filteredVariablesAndOrders.isEmpty()) return this@nthAntiderivativeWithRespectTo
+    LabeledPolynomial<C>(
+        buildMap(coefficients.size) {
+            coefficients
+                .forEach { (degs, c) ->
+                    val newDegs = buildMap<Symbol, UInt>(degs.size + 1) {
+                        for ((variable, order) in filteredVariablesAndOrders) put(variable, order)
+                        for ((vari, deg) in degs) put(vari, deg + getOrElse(vari) { 0u })
+                    }
+                    put(
+                        newDegs,
+                        filteredVariablesAndOrders.entries.fold(c) { acc1, (index, order) ->
+                            newDegs[index]!!.let { deg ->
+                                (deg downTo deg - order + 1u)
+                                    .fold(acc1) { acc2, ord -> acc2 / multiplyByDoubling(one, ord) }
+                            }
+                        }
+                    )
+                }
+        }
+    )
+}

kmath-functions/src/commonMain/kotlin/space/kscience/kmath/functions/listConstructors.kt

@@ -3,58 +3,95 @@
  * Use of this source code is governed by the Apache 2.0 license that can be found in the license/LICENSE.txt file.
  */
 
+/*
+ * Copyright 2018-2021 KMath contributors.
+ * Use of this source code is governed by the Apache 2.0 license that can be found in the license/LICENSE.txt file.
+ */
+
 package space.kscience.kmath.functions
 
 import space.kscience.kmath.operations.Ring
 
 
 /**
- * Returns a [ListPolynomial] instance with given [coefficients]. The collection of coefficients will be reversed if
- * [reverse] parameter is true.
+ * Constructs a [ListPolynomial] instance with provided [coefficients]. The collection of coefficients will be reversed
+ * if [reverse] parameter is true.
  */
 @Suppress("FunctionName")
 public fun <C> ListPolynomial(coefficients: List<C>, reverse: Boolean = false): ListPolynomial<C> =
     ListPolynomial(with(coefficients) { if (reverse) reversed() else this })
 
 /**
- * Returns a [ListPolynomial] instance with given [coefficients]. The collection of coefficients will be reversed if
- * [reverse] parameter is true.
+ * Constructs a [ListPolynomial] instance with provided [coefficients]. The collection of coefficients will be reversed
+ * if [reverse] parameter is true.
  */
 @Suppress("FunctionName")
 public fun <C> ListPolynomial(vararg coefficients: C, reverse: Boolean = false): ListPolynomial<C> =
     ListPolynomial(with(coefficients) { if (reverse) reversed() else toList() })
 
+/**
+ * Represents [this] constant as a [ListPolynomial].
+ */
 public fun <C> C.asListPolynomial() : ListPolynomial<C> = ListPolynomial(listOf(this))
 
 
 // Waiting for context receivers :( FIXME: Replace with context receivers when they will be available
 
+/**
+ * Constructs [ListRationalFunction] instance with numerator and denominator constructed with provided
+ * [numeratorCoefficients] and [denominatorCoefficients]. The both collections of coefficients will be reversed if
+ * [reverse] parameter is true.
+ */
 @Suppress("FunctionName")
 public fun <C> ListRationalFunction(numeratorCoefficients: List<C>, denominatorCoefficients: List<C>, reverse: Boolean = false): ListRationalFunction<C> =
     ListRationalFunction<C>(
         ListPolynomial( with(numeratorCoefficients) { if (reverse) reversed() else this } ),
         ListPolynomial( with(denominatorCoefficients) { if (reverse) reversed() else this } )
     )
-@Suppress("FunctionName")
-public fun <C, A: Ring<C>> ListRationalFunctionSpace<C, A>.ListRationalFunction(numerator: ListPolynomial<C>): ListRationalFunction<C> =
-    ListRationalFunction<C>(numerator, polynomialOne)
+/**
+ * Constructs [ListRationalFunction] instance with provided [numerator] and unit denominator.
+ */
 @Suppress("FunctionName")
 public fun <C, A: Ring<C>> A.ListRationalFunction(numerator: ListPolynomial<C>): ListRationalFunction<C> =
     ListRationalFunction<C>(numerator, ListPolynomial(listOf(one)))
+/**
+ * Constructs [ListRationalFunction] instance with provided [numerator] and unit denominator.
+ */
 @Suppress("FunctionName")
-public fun <C, A: Ring<C>> ListRationalFunctionSpace<C, A>.ListRationalFunction(numeratorCoefficients: List<C>, reverse: Boolean = false): ListRationalFunction<C> =
-    ListRationalFunction<C>(
-        ListPolynomial( with(numeratorCoefficients) { if (reverse) reversed() else this } ),
-        polynomialOne
-    )
+public fun <C, A: Ring<C>> ListRationalFunctionSpace<C, A>.ListRationalFunction(numerator: ListPolynomial<C>): ListRationalFunction<C> =
+    ListRationalFunction<C>(numerator, polynomialOne)
+/**
+ * Constructs [ListRationalFunction] instance with numerator constructed with provided [numeratorCoefficients] and unit
+ * denominator. The collection of numerator coefficients will be reversed if [reverse] parameter is true.
+ */
 @Suppress("FunctionName")
 public fun <C, A: Ring<C>> A.ListRationalFunction(numeratorCoefficients: List<C>, reverse: Boolean = false): ListRationalFunction<C> =
     ListRationalFunction<C>(
         ListPolynomial( with(numeratorCoefficients) { if (reverse) reversed() else this } ),
         ListPolynomial(listOf(one))
     )
+/**
+ * Constructs [ListRationalFunction] instance with numerator constructed with provided [numeratorCoefficients] and unit
+ * denominator. The collection of numerator coefficients will be reversed if [reverse] parameter is true.
+ */
+@Suppress("FunctionName")
+public fun <C, A: Ring<C>> ListRationalFunctionSpace<C, A>.ListRationalFunction(numeratorCoefficients: List<C>, reverse: Boolean = false): ListRationalFunction<C> =
+    ListRationalFunction<C>(
+        ListPolynomial( with(numeratorCoefficients) { if (reverse) reversed() else this } ),
+        polynomialOne
+    )
 
+/**
+ * Represents [this] constant as a rational function.
+ */ // FIXME: When context receivers will be ready, delete this function and uncomment the following two
+public fun <C, A: Ring<C>> C.asListRationalFunction(ring: A) : ListRationalFunction<C> = ring.ListRationalFunction(asListPolynomial())
+///**
+// * Represents [this] constant as a rational function.
+// */
 //context(A)
 //public fun <C, A: Ring<C>> C.asListRationalFunction() : ListRationalFunction<C> = ListRationalFunction(asListPolynomial())
+///**
+// * Represents [this] constant as a rational function.
+// */
 //context(ListRationalFunctionSpace<C, A>)
 //public fun <C, A: Ring<C>> C.asListRationalFunction() : ListRationalFunction<C> = ListRationalFunction(asListPolynomial())

kmath-functions/src/commonMain/kotlin/space/kscience/kmath/functions/listPolynomialUtil.kt

@@ -1,233 +0,0 @@
-/*
- * Copyright 2018-2021 KMath contributors.
- * Use of this source code is governed by the Apache 2.0 license that can be found in the license/LICENSE.txt file.
- */
-
-package space.kscience.kmath.functions
-
-import space.kscience.kmath.misc.UnstableKMathAPI
-import space.kscience.kmath.operations.*
-import kotlin.contracts.InvocationKind
-import kotlin.contracts.contract
-import kotlin.math.max
-import kotlin.math.min
-import kotlin.math.pow
-
-
-/**
- * Removes zeros on the end of the coefficient list of polynomial.
- */
-//context(PolynomialSpace<C, A>)
-//fun <C, A: Ring<C>> Polynomial<C>.removeZeros() : Polynomial<C> =
-//    if (degree > -1) Polynomial(coefficients.subList(0, degree + 1)) else zero
-
-/**
- * Creates a [ListPolynomialSpace] over a received ring.
- */
-public fun <C, A : Ring<C>> A.listPolynomial(): ListPolynomialSpace<C, A> =
-    ListPolynomialSpace(this)
-
-/**
- * Creates a [ListPolynomialSpace]'s scope over a received ring.
- */
-public inline fun <C, A : Ring<C>, R> A.listPolynomial(block: ListPolynomialSpace<C, A>.() -> R): R {
-    contract { callsInPlace(block, InvocationKind.EXACTLY_ONCE) }
-    return ListPolynomialSpace(this).block()
-}
-
-/**
- * Creates a [ScalableListPolynomialSpace] over a received scalable ring.
- */
-public fun <C, A> A.scalableListPolynomial(): ScalableListPolynomialSpace<C, A> where A : Ring<C>, A : ScaleOperations<C> =
-    ScalableListPolynomialSpace(this)
-
-/**
- * Creates a [ScalableListPolynomialSpace]'s scope over a received scalable ring.
- */
-public inline fun <C, A, R> A.scalableListPolynomial(block: ScalableListPolynomialSpace<C, A>.() -> R): R where A : Ring<C>, A : ScaleOperations<C> {
-    contract { callsInPlace(block, InvocationKind.EXACTLY_ONCE) }
-    return ScalableListPolynomialSpace(this).block()
-}
-
-@Suppress("NOTHING_TO_INLINE")
-internal inline fun <C> copyTo(
-    origin: List<C>,
-    originDegree: Int,
-    target: MutableList<C>,
-) {
-    for (deg in 0 .. originDegree) target[deg] = origin[deg]
-}
-
-@Suppress("NOTHING_TO_INLINE")
-internal inline fun <C> multiplyAddingToUpdater(
-    ring: Ring<C>,
-    multiplicand: MutableList<C>,
-    multiplicandDegree: Int,
-    multiplier: List<C>,
-    multiplierDegree: Int,
-    updater: MutableList<C>,
-    zero: C,
-) {
-    multiplyAddingTo(
-        ring = ring,
-        multiplicand = multiplicand,
-        multiplicandDegree = multiplicandDegree,
-        multiplier = multiplier,
-        multiplierDegree = multiplierDegree,
-        target = updater
-    )
-    for (updateDeg in 0 .. multiplicandDegree + multiplierDegree) {
-        multiplicand[updateDeg] = updater[updateDeg]
-        updater[updateDeg] = zero
-    }
-}
-
-@Suppress("NOTHING_TO_INLINE")
-internal inline fun <C> multiplyAddingTo(
-    ring: Ring<C>,
-    multiplicand: List<C>,
-    multiplicandDegree: Int,
-    multiplier: List<C>,
-    multiplierDegree: Int,
-    target: MutableList<C>
-) = ring {
-    for (d in 0 .. multiplicandDegree + multiplierDegree)
-        for (k in max(0, d - multiplierDegree)..min(multiplicandDegree, d))
-            target[d] += multiplicand[k] * multiplier[d - k]
-}
-
-/**
- * Evaluates the value of the given double polynomial for given double argument.
- */
-public fun ListPolynomial<Double>.substitute(arg: Double): Double =
-    coefficients.reduceIndexedOrNull { index, acc, c ->
-        acc + c * arg.pow(index)
-    } ?: .0
-
-/**
- * Evaluates the value of the given polynomial for given argument.
- *
- * It is an implementation of [Horner's method](https://en.wikipedia.org/wiki/Horner%27s_method).
- */
-public fun <C> ListPolynomial<C>.substitute(ring: Ring<C>, arg: C): C = ring {
-    if (coefficients.isEmpty()) return@ring zero
-    var result: C = coefficients.last()
-    for (j in coefficients.size - 2 downTo 0) {
-        result = (arg * result) + coefficients[j]
-    }
-    return result
-}
-
-public fun <C> ListPolynomial<C>.substitute(ring: Ring<C>, arg: ListPolynomial<C>) : ListPolynomial<C> = ring {
-    if (coefficients.isEmpty()) return ListPolynomial(emptyList())
-
-    val thisDegree = coefficients.lastIndex
-    if (thisDegree == -1) return ListPolynomial(emptyList())
-    val argDegree = arg.coefficients.lastIndex
-    if (argDegree == -1) return coefficients[0].asListPolynomial()
-    val constantZero = zero
-    val resultCoefs: MutableList<C> = MutableList(thisDegree * argDegree + 1) { constantZero }
-    resultCoefs[0] = coefficients[thisDegree]
-    val resultCoefsUpdate: MutableList<C> = MutableList(thisDegree * argDegree + 1) { constantZero }
-    var resultDegree = 0
-    for (deg in thisDegree - 1 downTo 0) {
-        resultCoefsUpdate[0] = coefficients[deg]
-        multiplyAddingToUpdater(
-            ring = ring,
-            multiplicand = resultCoefs,
-            multiplicandDegree = resultDegree,
-            multiplier = arg.coefficients,
-            multiplierDegree = argDegree,
-            updater = resultCoefsUpdate,
-            zero = constantZero
-        )
-        resultDegree += argDegree
-    }
-
-    return ListPolynomial<C>(resultCoefs)
-}
-
-/**
- * Represent the polynomial as a regular context-less function.
- */
-public fun <C, A : Ring<C>> ListPolynomial<C>.asFunction(ring: A): (C) -> C = { substitute(ring, it) }
-
-/**
- * Represent the polynomial as a regular context-less function.
- */
-public fun <C, A : Ring<C>> ListPolynomial<C>.asPolynomialFunctionOver(ring: A): (ListPolynomial<C>) -> ListPolynomial<C> = { substitute(ring, it) }
-
-/**
- * Returns algebraic derivative of received polynomial.
- */
-@UnstableKMathAPI
-public fun <C, A> ListPolynomial<C>.derivative(
-    algebra: A,
-): ListPolynomial<C> where  A : Ring<C>, A : NumericAlgebra<C> = algebra {
-    ListPolynomial(
-        buildList(max(0, coefficients.size - 1)) {
-            for (deg in 1 .. coefficients.lastIndex) add(number(deg) * coefficients[deg])
-        }
-    )
-}
-
-/**
- * Returns algebraic derivative of received polynomial.
- */
-@UnstableKMathAPI
-public fun <C, A> ListPolynomial<C>.nthDerivative(
-    algebra: A,
-    order: Int,
-): ListPolynomial<C> where A : Ring<C>, A : NumericAlgebra<C> = algebra {
-    require(order >= 0) { "Order of derivative must be non-negative" }
-    ListPolynomial(
-        buildList(max(0, coefficients.size - order)) {
-            for (deg in order.. coefficients.lastIndex)
-                add((deg - order + 1 .. deg).fold(coefficients[deg]) { acc, d -> acc * number(d) })
-        }
-    )
-}
-
-/**
- * Returns algebraic antiderivative of received polynomial.
- */
-@UnstableKMathAPI
-public fun <C, A> ListPolynomial<C>.antiderivative(
-    algebra: A,
-): ListPolynomial<C> where  A : Field<C>, A : NumericAlgebra<C> = algebra {
-    ListPolynomial(
-        buildList(coefficients.size + 1) {
-            add(zero)
-            coefficients.mapIndexedTo(this) { index, t -> t / number(index + 1) }
-        }
-    )
-}
-
-/**
- * Returns algebraic antiderivative of received polynomial.
- */
-@UnstableKMathAPI
-public fun <C, A> ListPolynomial<C>.nthAntiderivative(
-    algebra: A,
-    order: Int,
-): ListPolynomial<C> where  A : Field<C>, A : NumericAlgebra<C> = algebra {
-    require(order >= 0) { "Order of antiderivative must be non-negative" }
-    ListPolynomial(
-        buildList(coefficients.size + order) {
-            repeat(order) { add(zero) }
-            coefficients.mapIndexedTo(this) { index, c -> (1..order).fold(c) { acc, i -> acc / number(index + i) } }
-        }
-    )
-}
-
-/**
- * Compute a definite integral of a given polynomial in a [range]
- */
-@UnstableKMathAPI
-public fun <C : Comparable<C>> ListPolynomial<C>.integrate(
-    algebra: Field<C>,
-    range: ClosedRange<C>,
-): C = algebra {
-    val integral = antiderivative(algebra)
-    integral.substitute(algebra, range.endInclusive) - integral.substitute(algebra, range.start)
-}

kmath-functions/src/commonMain/kotlin/space/kscience/kmath/functions/listUtil.kt

@@ -0,0 +1,255 @@
+/*
+ * Copyright 2018-2021 KMath contributors.
+ * Use of this source code is governed by the Apache 2.0 license that can be found in the license/LICENSE.txt file.
+ */
+
+package space.kscience.kmath.functions
+
+import space.kscience.kmath.misc.UnstableKMathAPI
+import space.kscience.kmath.operations.*
+import kotlin.contracts.InvocationKind
+import kotlin.contracts.contract
+import kotlin.math.max
+import kotlin.math.pow
+
+
+/**
+ * Creates a [ListPolynomialSpace] over a received ring.
+ */
+public fun <C, A : Ring<C>> A.listPolynomialSpace(): ListPolynomialSpace<C, A> =
+    ListPolynomialSpace(this)
+
+/**
+ * Creates a [ListPolynomialSpace]'s scope over a received ring.
+ */ // TODO: When context will be ready move [ListPolynomialSpace] and add [A] to context receivers of [block]
+public inline fun <C, A : Ring<C>, R> A.listPolynomialSpace(block: ListPolynomialSpace<C, A>.() -> R): R {
+    contract { callsInPlace(block, InvocationKind.EXACTLY_ONCE) }
+    return ListPolynomialSpace(this).block()
+}
+
+/**
+ * Creates a [ScalableListPolynomialSpace] over a received scalable ring.
+ */
+public fun <C, A> A.scalableListPolynomialSpace(): ScalableListPolynomialSpace<C, A> where A : Ring<C>, A : ScaleOperations<C> =
+    ScalableListPolynomialSpace(this)
+
+/**
+ * Creates a [ScalableListPolynomialSpace]'s scope over a received scalable ring.
+ */ // TODO: When context will be ready move [ListPolynomialSpace] and add [A] to context receivers of [block]
+public inline fun <C, A, R> A.scalableListPolynomialSpace(block: ScalableListPolynomialSpace<C, A>.() -> R): R where A : Ring<C>, A : ScaleOperations<C> {
+    contract { callsInPlace(block, InvocationKind.EXACTLY_ONCE) }
+    return ScalableListPolynomialSpace(this).block()
+}
+
+/**
+ * Creates a [ListRationalFunctionSpace] over a received ring.
+ */
+public fun <C, A : Ring<C>> A.listRationalFunctionSpace(): ListRationalFunctionSpace<C, A> =
+    ListRationalFunctionSpace(this)
+
+/**
+ * Creates a [ListRationalFunctionSpace]'s scope over a received ring.
+ */ // TODO: When context will be ready move [ListRationalFunctionSpace] and add [A] to context receivers of [block]
+public inline fun <C, A : Ring<C>, R> A.listRationalFunctionSpace(block: ListRationalFunctionSpace<C, A>.() -> R): R {
+    contract { callsInPlace(block, InvocationKind.EXACTLY_ONCE) }
+    return ListRationalFunctionSpace(this).block()
+}
+
+
+/**
+ * Evaluates value of [this] Double polynomial on provided Double argument.
+ */
+public fun ListPolynomial<Double>.substitute(arg: Double): Double =
+    coefficients.reduceIndexedOrNull { index, acc, c ->
+        acc + c * arg.pow(index)
+    } ?: .0
+
+/**
+ * Evaluates value of [this] polynomial on provided argument.
+ *
+ * It is an implementation of [Horner's method](https://en.wikipedia.org/wiki/Horner%27s_method).
+ */
+public fun <C> ListPolynomial<C>.substitute(ring: Ring<C>, arg: C): C = ring {
+    if (coefficients.isEmpty()) return zero
+    var result: C = coefficients.last()
+    for (j in coefficients.size - 2 downTo 0) {
+        result = (arg * result) + coefficients[j]
+    }
+    return result
+}
+
+/**
+ * Substitutes provided polynomial [arg] into [this] polynomial.
+ *
+ * It is an implementation of [Horner's method](https://en.wikipedia.org/wiki/Horner%27s_method).
+ */ // TODO: To optimize boxing
+public fun <C> ListPolynomial<C>.substitute(ring: Ring<C>, arg: ListPolynomial<C>) : ListPolynomial<C> =
+    ring.listPolynomialSpace {
+        if (coefficients.isEmpty()) return zero
+        var result: ListPolynomial<C> = coefficients.last().asPolynomial()
+        for (j in coefficients.size - 2 downTo 0) {
+            result = (arg * result) + coefficients[j]
+        }
+        return result
+    }
+
+/**
+ * Substitutes provided rational function [arg] into [this] polynomial.
+ *
+ * It is an implementation of [Horner's method](https://en.wikipedia.org/wiki/Horner%27s_method).
+ */ // TODO: To optimize boxing
+public fun <C> ListPolynomial<C>.substitute(ring: Ring<C>, arg: ListRationalFunction<C>) : ListRationalFunction<C> =
+    ring.listRationalFunctionSpace {
+        if (coefficients.isEmpty()) return zero
+        var result: ListRationalFunction<C> = coefficients.last().asRationalFunction()
+        for (j in coefficients.size - 2 downTo 0) {
+            result = (arg * result) + coefficients[j]
+        }
+        return result
+    }
+
+/**
+ * Evaluates value of [this] Double rational function in provided Double argument.
+ */
+public fun ListRationalFunction<Double>.substitute(arg: Double): Double =
+    numerator.substitute(arg) / denominator.substitute(arg)
+
+/**
+ * Evaluates value of [this] polynomial for provided argument.
+ *
+ * It is an implementation of [Horner's method](https://en.wikipedia.org/wiki/Horner%27s_method).
+ */
+public fun <C> ListRationalFunction<C>.substitute(ring: Field<C>, arg: C): C = ring {
+    numerator.substitute(ring, arg) / denominator.substitute(ring, arg)
+}
+
+/**
+ * Substitutes provided polynomial [arg] into [this] rational function.
+ */ // TODO: To optimize boxing
+public fun <C> ListRationalFunction<C>.substitute(ring: Ring<C>, arg: ListPolynomial<C>) : ListRationalFunction<C> =
+    ring.listRationalFunctionSpace {
+        numerator.substitute(ring, arg) / denominator.substitute(ring, arg)
+    }
+
+/**
+ * Substitutes provided rational function [arg] into [this] rational function.
+ */ // TODO: To optimize boxing
+public fun <C> ListRationalFunction<C>.substitute(ring: Ring<C>, arg: ListRationalFunction<C>) : ListRationalFunction<C> =
+    ring.listRationalFunctionSpace {
+        numerator.substitute(ring, arg) / denominator.substitute(ring, arg)
+    }
+
+/**
+ * Represent [this] polynomial as a regular context-less function.
+ */
+public fun <C, A : Ring<C>> ListPolynomial<C>.asFunctionOver(ring: A): (C) -> C = { substitute(ring, it) }
+
+/**
+ * Represent [this] polynomial as a regular context-less function.
+ */
+public fun <C, A : Ring<C>> ListPolynomial<C>.asFunctionOfConstantOver(ring: A): (C) -> C = { substitute(ring, it) }
+
+/**
+ * Represent [this] polynomial as a regular context-less function.
+ */
+public fun <C, A : Ring<C>> ListPolynomial<C>.asFunctionOfPolynomialOver(ring: A): (ListPolynomial<C>) -> ListPolynomial<C> = { substitute(ring, it) }
+
+/**
+ * Represent [this] polynomial as a regular context-less function.
+ */
+public fun <C, A : Ring<C>> ListPolynomial<C>.asFunctionOfRationalFunctionOver(ring: A): (ListRationalFunction<C>) -> ListRationalFunction<C> = { substitute(ring, it) }
+
+/**
+ * Represent [this] rational function as a regular context-less function.
+ */
+public fun <C, A : Field<C>> ListRationalFunction<C>.asFunctionOver(ring: A): (C) -> C = { substitute(ring, it) }
+
+/**
+ * Represent [this] rational function as a regular context-less function.
+ */
+public fun <C, A : Field<C>> ListRationalFunction<C>.asFunctionOfConstantOver(ring: A): (C) -> C = { substitute(ring, it) }
+
+/**
+ * Represent [this] rational function as a regular context-less function.
+ */
+public fun <C, A : Ring<C>> ListRationalFunction<C>.asFunctionOfPolynomialOver(ring: A): (ListPolynomial<C>) -> ListRationalFunction<C> = { substitute(ring, it) }
+
+/**
+ * Represent [this] rational function as a regular context-less function.
+ */
+public fun <C, A : Ring<C>> ListRationalFunction<C>.asFunctionOfRationalFunctionOver(ring: A): (ListRationalFunction<C>) -> ListRationalFunction<C> = { substitute(ring, it) }
+
+/**
+ * Returns algebraic derivative of received polynomial.
+ */
+@UnstableKMathAPI
+public fun <C, A> ListPolynomial<C>.derivative(
+    ring: A,
+): ListPolynomial<C> where  A : Ring<C>, A : NumericAlgebra<C> = ring {
+    ListPolynomial(
+        buildList(max(0, coefficients.size - 1)) {
+            for (deg in 1 .. coefficients.lastIndex) add(number(deg) * coefficients[deg])
+        }
+    )
+}
+
+/**
+ * Returns algebraic derivative of received polynomial of specified [order]. The [order] should be non-negative integer.
+ */
+@UnstableKMathAPI
+public fun <C, A> ListPolynomial<C>.nthDerivative(
+    ring: A,
+    order: Int,
+): ListPolynomial<C> where A : Ring<C>, A : NumericAlgebra<C> = ring {
+    require(order >= 0) { "Order of derivative must be non-negative" }
+    ListPolynomial(
+        buildList(max(0, coefficients.size - order)) {
+            for (deg in order.. coefficients.lastIndex)
+                add((deg - order + 1 .. deg).fold(coefficients[deg]) { acc, d -> acc * number(d) })
+        }
+    )
+}
+
+/**
+ * Returns algebraic antiderivative of received polynomial.
+ */
+@UnstableKMathAPI
+public fun <C, A> ListPolynomial<C>.antiderivative(
+    ring: A,
+): ListPolynomial<C> where  A : Field<C>, A : NumericAlgebra<C> = ring {
+    ListPolynomial(
+        buildList(coefficients.size + 1) {
+            add(zero)
+            coefficients.mapIndexedTo(this) { index, t -> t / number(index + 1) }
+        }
+    )
+}
+
+/**
+ * Returns algebraic antiderivative of received polynomial of specified [order]. The [order] should be non-negative integer.
+ */
+@UnstableKMathAPI
+public fun <C, A> ListPolynomial<C>.nthAntiderivative(
+    ring: A,
+    order: Int,
+): ListPolynomial<C> where  A : Field<C>, A : NumericAlgebra<C> = ring {
+    require(order >= 0) { "Order of antiderivative must be non-negative" }
+    ListPolynomial(
+        buildList(coefficients.size + order) {
+            repeat(order) { add(zero) }
+            coefficients.mapIndexedTo(this) { index, c -> (1..order).fold(c) { acc, i -> acc / number(index + i) } }
+        }
+    )
+}
+
+/**
+ * Computes a definite integral of [this] polynomial in the specified [range].
+ */
+@UnstableKMathAPI
+public fun <C : Comparable<C>> ListPolynomial<C>.integrate(
+    ring: Field<C>,
+    range: ClosedRange<C>,
+): C = ring {
+    val antiderivative = antiderivative(ring)
+    antiderivative.substitute(ring, range.endInclusive) - antiderivative.substitute(ring, range.start)
+}

kmath-functions/src/commonMain/kotlin/space/kscience/kmath/functions/listUtilOptimized.kt

@@ -5,41 +5,91 @@
 
 package space.kscience.kmath.functions
 
-import space.kscience.kmath.operations.Field
 import space.kscience.kmath.operations.Ring
 import space.kscience.kmath.operations.invoke
-import kotlin.contracts.InvocationKind
-import kotlin.contracts.contract
 import kotlin.math.max
+import kotlin.math.min
 
 
-/**
- * Creates a [ListRationalFunctionSpace] over a received ring.
- */
-public fun <C, A : Ring<C>> A.listRationalFunction(): ListRationalFunctionSpace<C, A> =
-    ListRationalFunctionSpace(this)
-
-/**
- * Creates a [ListRationalFunctionSpace]'s scope over a received ring.
- */
-public inline fun <C, A : Ring<C>, R> A.listRationalFunction(block: ListRationalFunctionSpace<C, A>.() -> R): R {
-    contract { callsInPlace(block, InvocationKind.EXACTLY_ONCE) }
-    return ListRationalFunctionSpace(this).block()
+// TODO: Optimized copies of substitution and invocation
+@UnstablePolynomialBoxingOptimization
+@Suppress("NOTHING_TO_INLINE")
+internal inline fun <C> copyTo(
+    origin: List<C>,
+    originDegree: Int,
+    target: MutableList<C>,
+) {
+    for (deg in 0 .. originDegree) target[deg] = origin[deg]
 }
 
-/**
- * Evaluates the value of the given double polynomial for given double argument.
- */
-public fun ListRationalFunction<Double>.substitute(arg: Double): Double =
-    numerator.substitute(arg) / denominator.substitute(arg)
+@UnstablePolynomialBoxingOptimization
+@Suppress("NOTHING_TO_INLINE")
+internal inline fun <C> multiplyAddingToUpdater(
+    ring: Ring<C>,
+    multiplicand: MutableList<C>,
+    multiplicandDegree: Int,
+    multiplier: List<C>,
+    multiplierDegree: Int,
+    updater: MutableList<C>,
+    zero: C,
+) {
+    multiplyAddingTo(
+        ring = ring,
+        multiplicand = multiplicand,
+        multiplicandDegree = multiplicandDegree,
+        multiplier = multiplier,
+        multiplierDegree = multiplierDegree,
+        target = updater
+    )
+    for (updateDeg in 0 .. multiplicandDegree + multiplierDegree) {
+        multiplicand[updateDeg] = updater[updateDeg]
+        updater[updateDeg] = zero
+    }
+}
 
-/**
- * Evaluates the value of the given polynomial for given argument.
- *
- * It is an implementation of [Horner's method](https://en.wikipedia.org/wiki/Horner%27s_method).
- */
-public fun <C> ListRationalFunction<C>.substitute(ring: Field<C>, arg: C): C = ring {
-    numerator.substitute(ring, arg) / denominator.substitute(ring, arg)
+@UnstablePolynomialBoxingOptimization
+@Suppress("NOTHING_TO_INLINE")
+internal inline fun <C> multiplyAddingTo(
+    ring: Ring<C>,
+    multiplicand: List<C>,
+    multiplicandDegree: Int,
+    multiplier: List<C>,
+    multiplierDegree: Int,
+    target: MutableList<C>
+) = ring {
+    for (d in 0 .. multiplicandDegree + multiplierDegree)
+        for (k in max(0, d - multiplierDegree)..min(multiplicandDegree, d))
+            target[d] += multiplicand[k] * multiplier[d - k]
+}
+
+@UnstablePolynomialBoxingOptimization
+public fun <C> ListPolynomial<C>.substitute2(ring: Ring<C>, arg: ListPolynomial<C>) : ListPolynomial<C> = ring {
+    if (coefficients.isEmpty()) return ListPolynomial(emptyList())
+
+    val thisDegree = coefficients.lastIndex
+    if (thisDegree == -1) return ListPolynomial(emptyList())
+    val argDegree = arg.coefficients.lastIndex
+    if (argDegree == -1) return coefficients[0].asListPolynomial()
+    val constantZero = zero
+    val resultCoefs: MutableList<C> = MutableList(thisDegree * argDegree + 1) { constantZero }
+    resultCoefs[0] = coefficients[thisDegree]
+    val resultCoefsUpdate: MutableList<C> = MutableList(thisDegree * argDegree + 1) { constantZero }
+    var resultDegree = 0
+    for (deg in thisDegree - 1 downTo 0) {
+        resultCoefsUpdate[0] = coefficients[deg]
+        multiplyAddingToUpdater(
+            ring = ring,
+            multiplicand = resultCoefs,
+            multiplicandDegree = resultDegree,
+            multiplier = arg.coefficients,
+            multiplierDegree = argDegree,
+            updater = resultCoefsUpdate,
+            zero = constantZero
+        )
+        resultDegree += argDegree
+    }
+
+    return ListPolynomial<C>(resultCoefs)
 }
 
 /**
@@ -52,6 +102,7 @@ public fun <C> ListRationalFunction<C>.substitute(ring: Field<C>, arg: C): C = r
  *
  * Used in [ListPolynomial.substitute] and [ListRationalFunction.substitute] for performance optimisation.
  */ // TODO: Дописать
+@UnstablePolynomialBoxingOptimization
 internal fun <C> ListPolynomial<C>.substituteRationalFunctionTakeNumerator(ring: Ring<C>, arg: ListRationalFunction<C>): ListPolynomial<C> = ring {
     if (coefficients.isEmpty()) return ListPolynomial(emptyList())
 
@@ -197,25 +248,3 @@ internal fun <C> ListPolynomial<C>.substituteRationalFunctionTakeNumerator(ring:
         )
     )
 }
-
-//operator fun <T: Field<T>> RationalFunction<T>.invoke(arg: T): T = numerator(arg) / denominator(arg)
-//
-//fun <T: Field<T>> RationalFunction<T>.reduced(): RationalFunction<T> =
-//    polynomialGCD(numerator, denominator).let {
-//        RationalFunction(
-//            numerator / it,
-//            denominator / it
-//        )
-//    }
-
-///**
-// * Returns result of applying formal derivative to the polynomial.
-// *
-// * @param T Field where we are working now.
-// * @return Result of the operator.
-// */
-//fun <T: Ring<T>> RationalFunction<T>.derivative() =
-//    RationalFunction(
-//        numerator.derivative() * denominator - denominator.derivative() * numerator,
-//        denominator * denominator
-//    )

kmath-functions/src/commonMain/kotlin/space/kscience/kmath/functions/misc.kt

@@ -0,0 +1,32 @@
+/*
+ * Copyright 2018-2021 KMath contributors.
+ * Use of this source code is governed by the Apache 2.0 license that can be found in the license/LICENSE.txt file.
+ */
+
+package space.kscience.kmath.functions
+
+
+/**
+ * Marks operations that are going to be optimized reimplementations by reducing number of boxings but currently is
+ * under development and is not stable (or even ready to use).
+ */
+@RequiresOptIn(
+    message = "It's copy of operation with optimized boxing. It's currently unstable.",
+    level = RequiresOptIn.Level.ERROR
+)
+internal annotation class UnstablePolynomialBoxingOptimization
+
+/**
+ * Marks declarations that give access to internal entities of polynomials delicate structure. Thus, it allows to
+ * optimize performance a bit by skipping standard steps, but such skips may cause critical errors if something is
+ * implemented badly. Make sure you fully read and understand documentation and don't break internal contracts.
+ */
+@RequiresOptIn(
+    message = "This declaration gives access to delicate internal structure of polynomials. " +
+            "It allows to optimize performance by skipping unnecessary arguments check. " +
+            "But at the same time makes it easy to make a mistake " +
+            "that will cause wrong computation result or even runtime error. " +
+            "Make sure you fully read and understand documentation.",
+    level = RequiresOptIn.Level.WARNING
+)
+internal annotation class DelicatePolynomialAPI

kmath-functions/src/commonMain/kotlin/space/kscience/kmath/functions/numberedConstructors.kt

@@ -3,6 +3,8 @@
  * Use of this source code is governed by the Apache 2.0 license that can be found in the license/LICENSE.txt file.
  */
 
+@file:Suppress("FunctionName", "NOTHING_TO_INLINE")
+
 package space.kscience.kmath.functions
 
 import space.kscience.kmath.misc.UnstableKMathAPI
@@ -14,182 +16,474 @@ import space.kscience.kmath.operations.Ring
  */
 internal fun List<UInt>.cleanUp() = subList(0, indexOfLast { it != 0U } + 1)
 
-// Waiting for context receivers :( FIXME: Replace with context receivers when they will be available
+/**
+ * Constructs [NumberedPolynomial] with provided coefficients map [coefs]. The map is used as is.
+ */
+@PublishedApi
+internal inline fun <C> NumberedPolynomialAsIs(coefs: Map<List<UInt>, C>) : NumberedPolynomial<C> = NumberedPolynomial<C>(coefs)
 
-@Suppress("FunctionName", "NOTHING_TO_INLINE")
-internal inline fun <C, A: Ring<C>> NumberedPolynomialSpace<C, A>.NumberedPolynomial(coefs: Map<List<UInt>, C>, toCheckInput: Boolean = true) : NumberedPolynomial<C> = ring.NumberedPolynomial(coefs, toCheckInput)
-@Suppress("FunctionName", "NOTHING_TO_INLINE")
-internal inline fun <C, A: Ring<C>> NumberedRationalFunctionSpace<C, A>.NumberedPolynomial(coefs: Map<List<UInt>, C>, toCheckInput: Boolean = true) : NumberedPolynomial<C> = ring.NumberedPolynomial(coefs, toCheckInput)
-@Suppress("FunctionName")
-internal fun <C, A: Ring<C>> A.NumberedPolynomial(coefs: Map<List<UInt>, C>, toCheckInput: Boolean = true) : NumberedPolynomial<C> {
-    if (!toCheckInput) return NumberedPolynomial<C>(coefs)
+/**
+ * Constructs [NumberedPolynomial] with provided collection of [pairs] of pairs "term's signature &mdash; term's coefficient".
+ * The collections will be transformed to map with [toMap] and then will be used as is.
+ */
+@PublishedApi
+internal inline fun <C> NumberedPolynomialAsIs(pairs: Collection<Pair<List<UInt>, C>>) : NumberedPolynomial<C> = NumberedPolynomial<C>(pairs.toMap())
 
+/**
+ * Constructs [NumberedPolynomial] with provided array of [pairs] of pairs "term's signature &mdash; term's coefficient".
+ * The array will be transformed to map with [toMap] and then will be used as is.
+ */
+@PublishedApi
+internal inline fun <C> NumberedPolynomialAsIs(vararg pairs: Pair<List<UInt>, C>) : NumberedPolynomial<C> = NumberedPolynomial<C>(pairs.toMap())
+
+/**
+ * Constructs [NumberedPolynomial] with provided coefficients map [coefs]. The map is used as is.
+ *
+ * **Be sure you read description of [NumberedPolynomial.coefficients]. Otherwise, you may make a mistake that will
+ * cause wrong computation result or even runtime error.**
+ */
+@DelicatePolynomialAPI
+public inline fun <C> NumberedPolynomialWithoutCheck(coefs: Map<List<UInt>, C>) : NumberedPolynomial<C> = NumberedPolynomial<C>(coefs)
+
+/**
+ * Constructs [NumberedPolynomial] with provided collection of [pairs] of pairs "term's signature &mdash; term's coefficient".
+ * The collections will be transformed to map with [toMap] and then will be used as is.
+ *
+ * **Be sure you read description of [NumberedPolynomial.coefficients]. Otherwise, you may make a mistake that will
+ * cause wrong computation result or even runtime error.**
+ */
+@DelicatePolynomialAPI
+public inline fun <C> NumberedPolynomialWithoutCheck(pairs: Collection<Pair<List<UInt>, C>>) : NumberedPolynomial<C> = NumberedPolynomial<C>(pairs.toMap())
+
+/**
+ * Constructs [NumberedPolynomial] with provided array of [pairs] of pairs "term's signature &mdash; term's coefficient".
+ * The array will be transformed to map with [toMap] and then will be used as is.
+ *
+ * **Be sure you read description of [NumberedPolynomial.coefficients]. Otherwise, you may make a mistake that will
+ * cause wrong computation result or even runtime error.**
+ */
+@DelicatePolynomialAPI
+public inline fun <C> NumberedPolynomialWithoutCheck(vararg pairs: Pair<List<UInt>, C>) : NumberedPolynomial<C> = NumberedPolynomial<C>(pairs.toMap())
+
+/**
+ * Constructs [NumberedPolynomial] with provided coefficients map [coefs].
+ *
+ * [coefs] will be "cleaned up":
+ * 1. Zeros at the ends of terms' signatures (e.g. [coefs] keys) will be removed. (See [cleanUp].)
+ * 1. Terms that happen to have the same signature will be summed up.
+ * 1. New map will be formed of resulting terms.
+ */
+public fun <C> NumberedPolynomial(coefs: Map<List<UInt>, C>, add: (C, C) -> C) : NumberedPolynomial<C> {
     val fixedCoefs = mutableMapOf<List<UInt>, C>()
 
     for (entry in coefs) {
         val key = entry.key.cleanUp()
         val value = entry.value
-        fixedCoefs[key] = if (key in fixedCoefs) fixedCoefs[key]!! + value else value
+        fixedCoefs[key] = if (key in fixedCoefs) add(fixedCoefs[key]!!, value) else value
     }
 
     return NumberedPolynomial<C>(fixedCoefs)
 }
 
-@Suppress("FunctionName", "NOTHING_TO_INLINE")
-internal inline fun <C, A: Ring<C>> NumberedPolynomialSpace<C, A>.NumberedPolynomial(pairs: Collection<Pair<List<UInt>, C>>, toCheckInput: Boolean = true) : NumberedPolynomial<C> = ring.NumberedPolynomial(pairs, toCheckInput)
-@Suppress("FunctionName", "NOTHING_TO_INLINE")
-internal inline fun <C, A: Ring<C>> NumberedRationalFunctionSpace<C, A>.NumberedPolynomial(pairs: Collection<Pair<List<UInt>, C>>, toCheckInput: Boolean = true) : NumberedPolynomial<C> = ring.NumberedPolynomial(pairs, toCheckInput)
-@Suppress("FunctionName")
-internal fun <C, A: Ring<C>> A.NumberedPolynomial(pairs: Collection<Pair<List<UInt>, C>>, toCheckInput: Boolean = true) : NumberedPolynomial<C> {
-    if (!toCheckInput) return NumberedPolynomial<C>(pairs.toMap())
-
+/**
+ * Constructs [NumberedPolynomial] with provided collection of [pairs] of pairs "term's signature &mdash; term's coefficient".
+ *
+ * [pairs] will be "cleaned up":
+ * 1. Zeros at the ends of terms' signatures (e.g. [pairs] keys) will be removed. (See [cleanUp].)
+ * 1. Terms that happen to have the same signature will be summed up.
+ * 1. New map will be formed of resulting terms.
+ */
+public fun <C> NumberedPolynomial(pairs: Collection<Pair<List<UInt>, C>>, add: (C, C) -> C) : NumberedPolynomial<C> {
     val fixedCoefs = mutableMapOf<List<UInt>, C>()
 
     for (entry in pairs) {
         val key = entry.first.cleanUp()
         val value = entry.second
-        fixedCoefs[key] = if (key in fixedCoefs) fixedCoefs[key]!! + value else value
+        fixedCoefs[key] = if (key in fixedCoefs) add(fixedCoefs[key]!!, value) else value
     }
 
     return NumberedPolynomial<C>(fixedCoefs)
 }
 
-@Suppress("FunctionName", "NOTHING_TO_INLINE")
-internal inline fun <C, A: Ring<C>> NumberedPolynomialSpace<C, A>.NumberedPolynomial(vararg pairs: Pair<List<UInt>, C>, toCheckInput: Boolean = true) : NumberedPolynomial<C> = ring.NumberedPolynomial(pairs = pairs, toCheckInput = toCheckInput)
-@Suppress("FunctionName", "NOTHING_TO_INLINE")
-internal inline fun <C, A: Ring<C>> NumberedRationalFunctionSpace<C, A>.NumberedPolynomial(vararg pairs: Pair<List<UInt>, C>, toCheckInput: Boolean = true) : NumberedPolynomial<C> = ring.NumberedPolynomial(pairs = pairs, toCheckInput = toCheckInput)
-@Suppress("FunctionName")
-internal fun <C, A: Ring<C>> A.NumberedPolynomial(vararg pairs: Pair<List<UInt>, C>, toCheckInput: Boolean = true) : NumberedPolynomial<C> {
-    if (!toCheckInput) return NumberedPolynomial<C>(pairs.toMap())
-
+/**
+ * Constructs [NumberedPolynomial] with provided array [pairs] of pairs "term's signature &mdash; term's coefficient".
+ *
+ * [pairs] will be "cleaned up":
+ * 1. Zeros at the ends of terms' signatures (e.g. [pairs] keys) will be removed. (See [cleanUp].)
+ * 1. Terms that happen to have the same signature will be summed up.
+ * 1. New map will be formed of resulting terms.
+ */
+public fun <C> NumberedPolynomial(vararg pairs: Pair<List<UInt>, C>, add: (C, C) -> C) : NumberedPolynomial<C> {
     val fixedCoefs = mutableMapOf<List<UInt>, C>()
 
     for (entry in pairs) {
         val key = entry.first.cleanUp()
         val value = entry.second
-        fixedCoefs[key] = if (key in fixedCoefs) fixedCoefs[key]!! + value else value
+        fixedCoefs[key] = if (key in fixedCoefs) add(fixedCoefs[key]!!, value) else value
     }
 
     return NumberedPolynomial<C>(fixedCoefs)
 }
 
-@Suppress("FunctionName")
-public fun <C, A: Ring<C>> A.NumberedPolynomial(coefs: Map<List<UInt>, C>) : NumberedPolynomial<C> = NumberedPolynomial(coefs, toCheckInput = true)
-@Suppress("FunctionName")
-public fun <C, A: Ring<C>> NumberedPolynomialSpace<C, A>.NumberedPolynomial(coefs: Map<List<UInt>, C>) : NumberedPolynomial<C> = NumberedPolynomial(coefs, toCheckInput = true)
-@Suppress("FunctionName")
-public fun <C, A: Ring<C>> NumberedRationalFunctionSpace<C, A>.NumberedPolynomial(coefs: Map<List<UInt>, C>) : NumberedPolynomial<C> = NumberedPolynomial(coefs, toCheckInput = true)
+// Waiting for context receivers :( FIXME: Replace with context receivers when they will be available
 
-@Suppress("FunctionName")
-public fun <C, A: Ring<C>> A.NumberedPolynomial(pairs: Collection<Pair<List<UInt>, C>>) : NumberedPolynomial<C> = NumberedPolynomial(pairs, toCheckInput = true)
-@Suppress("FunctionName")
-public fun <C, A: Ring<C>> NumberedPolynomialSpace<C, A>.NumberedPolynomial(pairs: Collection<Pair<List<UInt>, C>>) : NumberedPolynomial<C> = NumberedPolynomial(pairs, toCheckInput = true)
-@Suppress("FunctionName")
-public fun <C, A: Ring<C>> NumberedRationalFunctionSpace<C, A>.NumberedPolynomial(pairs: Collection<Pair<List<UInt>, C>>) : NumberedPolynomial<C> = NumberedPolynomial(pairs, toCheckInput = true)
+/**
+ * Constructs [NumberedPolynomial] with provided coefficients map [coefs].
+ *
+ * [coefs] will be "cleaned up":
+ * 1. Zeros at the ends of terms' signatures (e.g. [coefs] keys) will be removed. (See [cleanUp].)
+ * 1. Terms that happen to have the same signature will be summed up.
+ * 1. New map will be formed of resulting terms.
+ */
+public inline fun <C, A: Ring<C>> A.NumberedPolynomial(coefs: Map<List<UInt>, C>) : NumberedPolynomial<C> = NumberedPolynomial(coefs, ::add)
+/**
+ * Constructs [NumberedPolynomial] with provided coefficients map [coefs].
+ *
+ * [coefs] will be "cleaned up":
+ * 1. Zeros at the ends of terms' signatures (e.g. [coefs] keys) will be removed. (See [cleanUp].)
+ * 1. Terms that happen to have the same signature will be summed up.
+ * 1. New map will be formed of resulting terms.
+ */
+public inline fun <C, A: Ring<C>> NumberedPolynomialSpace<C, A>.NumberedPolynomial(coefs: Map<List<UInt>, C>) : NumberedPolynomial<C> = NumberedPolynomial(coefs) { left: C, right: C -> left + right }
 
-@Suppress("FunctionName")
-public fun <C, A: Ring<C>> A.NumberedPolynomial(vararg pairs: Pair<List<UInt>, C>) : NumberedPolynomial<C> = NumberedPolynomial(*pairs, toCheckInput = true)
-@Suppress("FunctionName")
-public fun <C, A: Ring<C>> NumberedPolynomialSpace<C, A>.NumberedPolynomial(vararg pairs: Pair<List<UInt>, C>) : NumberedPolynomial<C> = NumberedPolynomial(*pairs, toCheckInput = true)
-@Suppress("FunctionName")
-public fun <C, A: Ring<C>> NumberedRationalFunctionSpace<C, A>.NumberedPolynomial(vararg pairs: Pair<List<UInt>, C>) : NumberedPolynomial<C> = NumberedPolynomial(*pairs, toCheckInput = true)
+/**
+ * Constructs [NumberedPolynomial] with provided coefficients map [coefs].
+ *
+ * [coefs] will be "cleaned up":
+ * 1. Zeros at the ends of terms' signatures (e.g. [coefs] keys) will be removed. (See [cleanUp].)
+ * 1. Terms that happen to have the same signature will be summed up.
+ * 1. New map will be formed of resulting terms.
+ */
+public inline fun <C, A: Ring<C>> NumberedRationalFunctionSpace<C, A>.NumberedPolynomial(coefs: Map<List<UInt>, C>) : NumberedPolynomial<C> = NumberedPolynomial(coefs) { left: C, right: C -> left + right }
 
-public fun <C> C.asNumberedPolynomial() : NumberedPolynomial<C> = NumberedPolynomial<C>(mapOf(emptyList<UInt>() to this))
+/**
+ * Constructs [NumberedPolynomial] with provided collection of [pairs] of pairs "term's signature &mdash; term's coefficient".
+ *
+ * [pairs] will be "cleaned up":
+ * 1. Zeros at the ends of terms' signatures (e.g. [pairs] keys) will be removed. (See [cleanUp].)
+ * 1. Terms that happen to have the same signature will be summed up.
+ * 1. New map will be formed of resulting terms.
+ */
+public inline fun <C, A: Ring<C>> A.NumberedPolynomial(pairs: Collection<Pair<List<UInt>, C>>) : NumberedPolynomial<C> = NumberedPolynomial(pairs, ::add)
 
+/**
+ * Constructs [NumberedPolynomial] with provided collection of [pairs] of pairs "term's signature &mdash; term's coefficient".
+ *
+ * [pairs] will be "cleaned up":
+ * 1. Zeros at the ends of terms' signatures (e.g. [pairs] keys) will be removed. (See [cleanUp].)
+ * 1. Terms that happen to have the same signature will be summed up.
+ * 1. New map will be formed of resulting terms.
+ */
+public inline fun <C, A: Ring<C>> NumberedPolynomialSpace<C, A>.NumberedPolynomial(pairs: Collection<Pair<List<UInt>, C>>) : NumberedPolynomial<C> = NumberedPolynomial(pairs) { left: C, right: C -> left + right }
+/**
+ * Constructs [NumberedPolynomial] with provided collection of [pairs] of pairs "term's signature &mdash; term's coefficient".
+ *
+ * [pairs] will be "cleaned up":
+ * 1. Zeros at the ends of terms' signatures (e.g. [pairs] keys) will be removed. (See [cleanUp].)
+ * 1. Terms that happen to have the same signature will be summed up.
+ * 1. New map will be formed of resulting terms.
+ */
+public inline fun <C, A: Ring<C>> NumberedRationalFunctionSpace<C, A>.NumberedPolynomial(pairs: Collection<Pair<List<UInt>, C>>) : NumberedPolynomial<C> = NumberedPolynomial(pairs) { left: C, right: C -> left + right }
+
+/**
+ * Constructs [NumberedPolynomial] with provided array [pairs] of pairs "term's signature &mdash; term's coefficient".
+ *
+ * [pairs] will be "cleaned up":
+ * 1. Zeros at the ends of terms' signatures (e.g. [pairs] keys) will be removed. (See [cleanUp].)
+ * 1. Terms that happen to have the same signature will be summed up.
+ * 1. New map will be formed of resulting terms.
+ */
+public inline fun <C, A: Ring<C>> A.NumberedPolynomial(vararg pairs: Pair<List<UInt>, C>) : NumberedPolynomial<C> = NumberedPolynomial(*pairs) { left: C, right: C -> left + right }
+/**
+ * Constructs [NumberedPolynomial] with provided array [pairs] of pairs "term's signature &mdash; term's coefficient".
+ *
+ * [pairs] will be "cleaned up":
+ * 1. Zeros at the ends of terms' signatures (e.g. [pairs] keys) will be removed. (See [cleanUp].)
+ * 1. Terms that happen to have the same signature will be summed up.
+ * 1. New map will be formed of resulting terms.
+ */
+public inline fun <C, A: Ring<C>> NumberedPolynomialSpace<C, A>.NumberedPolynomial(vararg pairs: Pair<List<UInt>, C>) : NumberedPolynomial<C> = NumberedPolynomial(*pairs) { left: C, right: C -> left + right }
+/**
+ * Constructs [NumberedPolynomial] with provided array [pairs] of pairs "term's signature &mdash; term's coefficient".
+ *
+ * [pairs] will be "cleaned up":
+ * 1. Zeros at the ends of terms' signatures (e.g. [pairs] keys) will be removed. (See [cleanUp].)
+ * 1. Terms that happen to have the same signature will be summed up.
+ * 1. New map will be formed of resulting terms.
+ */
+public inline fun <C, A: Ring<C>> NumberedRationalFunctionSpace<C, A>.NumberedPolynomial(vararg pairs: Pair<List<UInt>, C>) : NumberedPolynomial<C> = NumberedPolynomial(*pairs) { left: C, right: C -> left + right }
+
+/**
+ * Converts [this] constant to [NumberedPolynomial].
+ */
+public inline fun <C> C.asNumberedPolynomial() : NumberedPolynomial<C> = NumberedPolynomialAsIs(mapOf(emptyList<UInt>() to this))
+
+/**
+ * Marks DSL that allows to more simply create [NumberedPolynomial]s with good performance.
+ *
+ * For example, polynomial `5 x_1^2 x_3^3 - 6 x_2` can be described as
+ * ```
+ * Int.algebra {
+ *     val numberedPolynomial : NumberedPolynomial<Int> = NumberedPolynomial {
+ *         5 { 1 inPowerOf 2u; 3 inPowerOf 3u } // 5 x_1^2 x_3^3 +
+ *         (-6) { 2 inPowerOf 1u }              // (-6) x_2^1
+ *     }
+ * }
+ * ```
+ */
 @DslMarker
 @UnstableKMathAPI
 internal annotation class NumberedPolynomialConstructorDSL
 
+/**
+ * Builder of [NumberedPolynomial] signature. It should be used as an implicit context for lambdas that describe term signature.
+ */
 @UnstableKMathAPI
 @NumberedPolynomialConstructorDSL
 public class NumberedPolynomialTermSignatureBuilder {
+    /**
+     * Signature storage. Any declaration of any variable's power updates the storage by increasing corresponding value.
+     * Afterward the storage will be used as a resulting signature.
+     */
     private val signature: MutableList<UInt> = ArrayList()
-    public fun build(): List<UInt> = signature
+
+    /**
+     * Builds the resulting signature.
+     *
+     * In fact, it just returns [signature] as regular signature of type `List<UInt>`.
+     */
+    @PublishedApi
+    internal fun build(): List<UInt> = signature
+
+    /**
+     * Declares power of variable #[this] of degree [deg].
+     *
+     * Declaring another power of the same variable will increase its degree by received degree.
+     */
     public infix fun Int.inPowerOf(deg: UInt) {
-        if (this > signature.lastIndex) {
-            signature.addAll(List(this - signature.lastIndex - 1) { 0u })
+        val index = this - 1
+        if (index > signature.lastIndex) {
+            signature.addAll(List(index - signature.lastIndex - 1) { 0u })
             signature.add(deg)
         } else {
-            signature[this] = deg
+            signature[index] += deg
         }
     }
+    /**
+     * Declares power of variable #[this] of degree [deg].
+     *
+     * Declaring another power of the same variable will increase its degree by received degree.
+     */
     @Suppress("NOTHING_TO_INLINE")
     public inline infix fun Int.pow(deg: UInt): Unit = this inPowerOf deg
+    /**
+     * Declares power of variable #[this] of degree [deg].
+     *
+     * Declaring another power of the same variable will increase its degree by received degree.
+     */
     @Suppress("NOTHING_TO_INLINE")
     public inline infix fun Int.`in`(deg: UInt): Unit = this inPowerOf deg
+    /**
+     * Declares power of variable #[this] of degree [deg].
+     *
+     * Declaring another power of the same variable will increase its degree by received degree.
+     */
     @Suppress("NOTHING_TO_INLINE")
     public inline infix fun Int.of(deg: UInt): Unit = this inPowerOf deg
 }
 
+/**
+ * Builder of [NumberedPolynomial]. It should be used as an implicit context for lambdas that describe [NumberedPolynomial].
+ */
 @UnstableKMathAPI
-public class NumberedPolynomialBuilder<C>(private val zero: C, private val add: (C, C) -> C, capacity: Int = 0) {
-    private val coefficients: MutableMap<List<UInt>, C> = LinkedHashMap(capacity)
-    public fun build(): NumberedPolynomial<C> = NumberedPolynomial<C>(coefficients)
-    public operator fun C.invoke(block: NumberedPolynomialTermSignatureBuilder.() -> Unit) {
-        val signature = NumberedPolynomialTermSignatureBuilder().apply(block).build()
-        coefficients[signature] = add(coefficients.getOrElse(signature) { zero }, this@invoke)
+@NumberedPolynomialConstructorDSL
+public class NumberedPolynomialBuilder<C>(
+    /**
+     * Summation operation that will be used to sum coefficients of monomials of same signatures.
+     */
+    private val add: (C, C) -> C,
+    /**
+     * Initial capacity of coefficients map.
+     */
+    initialCapacity: Int = 0
+) {
+    /**
+     * Coefficients storage. Any declaration of any monomial updates the storage.
+     * Afterward the storage will be used as a resulting coefficients map.
+     */
+    private val coefficients: MutableMap<List<UInt>, C> = LinkedHashMap(initialCapacity)
+
+    /**
+     * Builds the resulting coefficients map.
+     *
+     * In fact, it just returns [coefficients] as regular coefficients map of type `Map<List<UInt>, C>`.
+     */
+    @PublishedApi
+    internal fun build(): NumberedPolynomial<C> = NumberedPolynomial<C>(coefficients)
+
+    /**
+     * Declares monomial with [this] coefficient and provided [signature].
+     *
+     * Declaring another monomial with the same signature will add [this] coefficient to existing one. If the sum of such
+     * coefficients is zero at any moment the monomial won't be removed but will be left as it is.
+     */
+    public infix fun C.with(signature: List<UInt>) {
+        coefficients[signature] = if (signature in coefficients) add(coefficients[signature]!!, this@with) else this@with
     }
+    /**
+     * Declares monomial with [this] coefficient and signature constructed by [block].
+     *
+     * Declaring another monomial with the same signature will add [this] coefficient to existing one. If the sum of such
+     * coefficients is zero at any moment the monomial won't be removed but will be left as it is.
+     */
     @Suppress("NOTHING_TO_INLINE")
     public inline infix fun C.with(noinline block: NumberedPolynomialTermSignatureBuilder.() -> Unit): Unit = this.invoke(block)
-    @Suppress("NOTHING_TO_INLINE")
-    public inline infix fun (NumberedPolynomialTermSignatureBuilder.() -> Unit).with(coef: C): Unit = coef.invoke(this)
-    @Suppress("NOTHING_TO_INLINE")
-    public infix fun sig(block: NumberedPolynomialTermSignatureBuilder.() -> Unit): NumberedPolynomialTermSignatureBuilder.() -> Unit = block
+    /**
+     * Declares monomial with [this] coefficient and signature constructed by [block].
+     *
+     * Declaring another monomial with the same signature will add [this] coefficient to existing one. If the sum of such
+     * coefficients is zero at any moment the monomial won't be removed but will be left as it is.
+     */
+    public inline operator fun C.invoke(block: NumberedPolynomialTermSignatureBuilder.() -> Unit): Unit =
+        this with NumberedPolynomialTermSignatureBuilder().apply(block).build()
 }
 
 // Waiting for context receivers :( FIXME: Replace with context receivers when they will be available
 
+///**
+// * Creates [NumberedPolynomial] with lambda [block] in context of [this] ring of constants.
+// *
+// * For example, polynomial `5 x_1^2 x_3^3 - 6 x_2` can be described as
+// * ```
+// * Int.algebra {
+// *     val numberedPolynomial : NumberedPolynomial<Int> = NumberedPolynomial {
+// *         5 { 1 inPowerOf 2u; 3 inPowerOf 3u } // 5 x_1^2 x_3^3 +
+// *         (-6) { 2 inPowerOf 1u }              // (-6) x_2^1
+// *     }
+// * }
+// * ```
+// */
+// FIXME: For now this fabric does not let next two fabrics work. (See KT-52803.) Possible feature solutions:
+//  1. `LowPriorityInOverloadResolution` becomes public. Then it should be applied to this function.
+//  2. Union types are implemented. Then all three functions should be rewritten
+//     as one with single union type as a (context) receiver.
+//@UnstableKMathAPI
+//public inline fun <C, A: Ring<C>> A.NumberedPolynomial(initialCapacity: Int = 0, block: NumberedPolynomialBuilder<C>.() -> Unit) : NumberedPolynomial<C> = NumberedPolynomialBuilder(::add, initialCapacity).apply(block).build()
+/**
+ * Creates [NumberedPolynomial] with lambda [block] in context of [this] ring of [NumberedPolynomial]s.
+ *
+ * For example, polynomial `5 x_1^2 x_3^3 - 6 x_2` can be described as
+ * ```
+ * Int.algebra {
+ *     val numberedPolynomial : NumberedPolynomial<Int> = NumberedPolynomial {
+ *         5 { 1 inPowerOf 2u; 3 inPowerOf 3u } // 5 x_1^2 x_3^3 +
+ *         (-6) { 2 inPowerOf 1u }              // (-6) x_2^1
+ *     }
+ * }
+ * ```
+ */
 @UnstableKMathAPI
-@NumberedPolynomialConstructorDSL
-@Suppress("FunctionName")
-public inline fun <C, A: Ring<C>> A.NumberedPolynomial(block: NumberedPolynomialBuilder<C>.() -> Unit) : NumberedPolynomial<C> = NumberedPolynomialBuilder(zero, ::add).apply(block).build()
+public inline fun <C, A: Ring<C>> NumberedPolynomialSpace<C, A>.NumberedPolynomial(initialCapacity: Int = 0, block: NumberedPolynomialBuilder<C>.() -> Unit) : NumberedPolynomial<C> = NumberedPolynomialBuilder({ left: C, right: C -> left + right }, initialCapacity).apply(block).build()
+/**
+ * Creates [NumberedPolynomial] with lambda [block] in context of [this] field of [NumberedRationalFunction]s.
+ *
+ * For example, polynomial `5 x_1^2 x_3^3 - 6 x_2` can be described as
+ * ```
+ * Int.algebra {
+ *     val numberedPolynomial : NumberedPolynomial<Int> = NumberedPolynomial {
+ *         5 { 1 inPowerOf 2u; 3 inPowerOf 3u } // 5 x_1^2 x_3^3 +
+ *         (-6) { 2 inPowerOf 1u }              // (-6) x_2^1
+ *     }
+ * }
+ * ```
+ */
 @UnstableKMathAPI
-@NumberedPolynomialConstructorDSL
-@Suppress("FunctionName")
-public inline fun <C, A: Ring<C>> A.NumberedPolynomial(capacity: Int, block: NumberedPolynomialBuilder<C>.() -> Unit) : NumberedPolynomial<C> = NumberedPolynomialBuilder(zero, ::add, capacity).apply(block).build()
-@UnstableKMathAPI
-@NumberedPolynomialConstructorDSL
-@Suppress("FunctionName")
-public inline fun <C, A: Ring<C>> NumberedPolynomialSpace<C, A>.NumberedPolynomial(block: NumberedPolynomialBuilder<C>.() -> Unit) : NumberedPolynomial<C> = NumberedPolynomialBuilder(constantZero, { left: C, right: C -> left + right}).apply(block).build()
-@UnstableKMathAPI
-@NumberedPolynomialConstructorDSL
-@Suppress("FunctionName")
-public inline fun <C, A: Ring<C>> NumberedPolynomialSpace<C, A>.NumberedPolynomial(capacity: Int, block: NumberedPolynomialBuilder<C>.() -> Unit) : NumberedPolynomial<C> = NumberedPolynomialBuilder(constantZero, { left: C, right: C -> left + right}, capacity).apply(block).build()
+public inline fun <C, A: Ring<C>> NumberedRationalFunctionSpace<C, A>.NumberedPolynomial(initialCapacity: Int = 0, block: NumberedPolynomialBuilder<C>.() -> Unit) : NumberedPolynomial<C> = NumberedPolynomialBuilder({ left: C, right: C -> left + right }, initialCapacity).apply(block).build()
 
 // Waiting for context receivers :( FIXME: Replace with context receivers when they will be available
 
-@Suppress("FunctionName")
-public fun <C, A: Ring<C>> NumberedRationalFunctionSpace<C, A>.NumberedRationalFunction(numeratorCoefficients: Map<List<UInt>, C>, denominatorCoefficients: Map<List<UInt>, C>): NumberedRationalFunction<C> =
-    NumberedRationalFunction<C>(
-        NumberedPolynomial(numeratorCoefficients, toCheckInput = true),
-        NumberedPolynomial(denominatorCoefficients, toCheckInput = true)
-    )
-@Suppress("FunctionName")
+/**
+ * Constructs [NumberedRationalFunction] with provided coefficients maps [numeratorCoefficients] and [denominatorCoefficients].
+ *
+ * The maps will be "cleaned up":
+ * 1. Zeros at the ends of terms' signatures (e.g. the maps' keys) will be removed. (See [cleanUp].)
+ * 1. Terms that happen to have the same signature will be summed up.
+ * 1. New map will be formed of resulting terms.
+ */
 public fun <C, A: Ring<C>> A.NumberedRationalFunction(numeratorCoefficients: Map<List<UInt>, C>, denominatorCoefficients: Map<List<UInt>, C>): NumberedRationalFunction<C> =
     NumberedRationalFunction<C>(
-        NumberedPolynomial(numeratorCoefficients, toCheckInput = true),
-        NumberedPolynomial(denominatorCoefficients, toCheckInput = true)
+        NumberedPolynomial(numeratorCoefficients),
+        NumberedPolynomial(denominatorCoefficients)
     )
-@Suppress("FunctionName")
-public fun <C, A: Ring<C>> NumberedRationalFunctionSpace<C, A>.NumberedRationalFunction(numerator: NumberedPolynomial<C>): NumberedRationalFunction<C> =
-    NumberedRationalFunction<C>(numerator, polynomialOne)
-@Suppress("FunctionName")
-public fun <C, A: Ring<C>> A.NumberedRationalFunction(numerator: NumberedPolynomial<C>): NumberedRationalFunction<C> =
-    NumberedRationalFunction<C>(numerator, NumberedPolynomial(mapOf(emptyList<UInt>() to one), toCheckInput = false))
-@Suppress("FunctionName")
-public fun <C, A: Ring<C>> NumberedRationalFunctionSpace<C, A>.NumberedRationalFunction(numeratorCoefficients: Map<List<UInt>, C>): NumberedRationalFunction<C> =
+/**
+ * Constructs [NumberedRationalFunction] with provided coefficients maps [numeratorCoefficients] and [denominatorCoefficients].
+ *
+ * The maps will be "cleaned up":
+ * 1. Zeros at the ends of terms' signatures (e.g. the maps' keys) will be removed. (See [cleanUp].)
+ * 1. Terms that happen to have the same signature will be summed up.
+ * 1. New map will be formed of resulting terms.
+ */
+public fun <C, A: Ring<C>> NumberedRationalFunctionSpace<C, A>.NumberedRationalFunction(numeratorCoefficients: Map<List<UInt>, C>, denominatorCoefficients: Map<List<UInt>, C>): NumberedRationalFunction<C> =
     NumberedRationalFunction<C>(
-        NumberedPolynomial(numeratorCoefficients, toCheckInput = true),
-        polynomialOne
-    )
-@Suppress("FunctionName")
-public fun <C, A: Ring<C>> A.NumberedRationalFunction(numeratorCoefficients: Map<List<UInt>, C>): NumberedRationalFunction<C> =
-    NumberedRationalFunction<C>(
-        NumberedPolynomial(numeratorCoefficients, toCheckInput = true),
-        NumberedPolynomial(mapOf(emptyList<UInt>() to one), toCheckInput = false)
+        NumberedPolynomial(numeratorCoefficients),
+        NumberedPolynomial(denominatorCoefficients)
     )
 
+/**
+ * Constructs [NumberedRationalFunction] with provided [numerator] and unit denominator.
+ */
+public fun <C, A: Ring<C>> A.NumberedRationalFunction(numerator: NumberedPolynomial<C>): NumberedRationalFunction<C> =
+    NumberedRationalFunction<C>(numerator, NumberedPolynomial(mapOf(emptyList<UInt>() to one)))
+/**
+ * Constructs [NumberedRationalFunction] with provided [numerator] and unit denominator.
+ */
+public fun <C, A: Ring<C>> NumberedRationalFunctionSpace<C, A>.NumberedRationalFunction(numerator: NumberedPolynomial<C>): NumberedRationalFunction<C> =
+    NumberedRationalFunction<C>(numerator, polynomialOne)
+
+/**
+ * Constructs [NumberedRationalFunction] with provided coefficients map [numeratorCoefficients] for numerator and unit
+ * denominator.
+ *
+ * [numeratorCoefficients] will be "cleaned up":
+ * 1. Zeros at the ends of terms' signatures (e.g. [numeratorCoefficients]'s keys) will be removed. (See [cleanUp].)
+ * 1. Terms that happen to have the same signature will be summed up.
+ * 1. New map will be formed of resulting terms.
+ */
+public fun <C, A: Ring<C>> NumberedRationalFunctionSpace<C, A>.NumberedRationalFunction(numeratorCoefficients: Map<List<UInt>, C>): NumberedRationalFunction<C> =
+    NumberedRationalFunction<C>(
+        NumberedPolynomial(numeratorCoefficients),
+        polynomialOne
+    )
+/**
+ * Constructs [NumberedRationalFunction] with provided coefficients map [numeratorCoefficients] for numerator and unit
+ * denominator.
+ *
+ * [numeratorCoefficients] will be "cleaned up":
+ * 1. Zeros at the ends of terms' signatures (e.g. [numeratorCoefficients]'s keys) will be removed. (See [cleanUp].)
+ * 1. Terms that happen to have the same signature will be summed up.
+ * 1. New map will be formed of resulting terms.
+ */
+public fun <C, A: Ring<C>> A.NumberedRationalFunction(numeratorCoefficients: Map<List<UInt>, C>): NumberedRationalFunction<C> =
+    NumberedRationalFunction<C>(
+        NumberedPolynomial(numeratorCoefficients),
+        NumberedPolynomialAsIs(mapOf(emptyList<UInt>() to one))
+    )
+
+///**
+// * Converts [this] constant to [NumberedRationalFunction].
+// */
 //context(A)
-//public fun <C, A: Ring<C>> C.asNumberedRationalFunction() : NumberedRationalFunction<C> = NumberedRationalFunction(asLabeledPolynomial())
+//public fun <C, A: Ring<C>> C.asNumberedRationalFunction() : NumberedRationalFunction<C> =
+//    NumberedRationalFunction(
+//        NumberedPolynomialAsIs(mapOf(emptyList<UInt>() to this)),
+//        NumberedPolynomialAsIs(mapOf(emptyList<UInt>() to one))
+//    )
+///**
+// * Converts [this] constant to [NumberedRationalFunction].
+// */
 //context(NumberedRationalFunctionSpace<C, A>)
-//public fun <C, A: Ring<C>> C.asNumberedRationalFunction() : NumberedRationalFunction<C> = NumberedRationalFunction(asLabeledPolynomial())
+//public fun <C, A: Ring<C>> C.asNumberedRationalFunction() : NumberedRationalFunction<C> =
+//    NumberedRationalFunction(
+//        NumberedPolynomialAsIs(mapOf(emptyList<UInt>() to this)),
+//        NumberedPolynomialAsIs(mapOf(emptyList<UInt>() to constantOne))
+//    )

kmath-functions/src/commonMain/kotlin/space/kscience/kmath/functions/numberedPolynomialUtil.kt

@@ -1,528 +0,0 @@
-package space.kscience.kmath.functions
-
-import space.kscience.kmath.misc.UnstableKMathAPI
-import space.kscience.kmath.operations.*
-import kotlin.contracts.*
-import kotlin.jvm.JvmName
-import kotlin.math.max
-
-
-// TODO: Docs
-
-/**
- * Creates a [NumberedPolynomialSpace] over a received ring.
- */
-public fun <C, A : Ring<C>> A.numberedPolynomial(): NumberedPolynomialSpace<C, A> =
-    NumberedPolynomialSpace(this)
-
-/**
- * Creates a [NumberedPolynomialSpace]'s scope over a received ring.
- */
-@OptIn(ExperimentalContracts::class)
-public inline fun <C, A : Ring<C>, R> A.numberedPolynomial(block: NumberedPolynomialSpace<C, A>.() -> R): R {
-    contract { callsInPlace(block, InvocationKind.EXACTLY_ONCE) }
-    return NumberedPolynomialSpace(this).block()
-}
-
-///**
-// * Represents the polynomial as a [String] where name of variable with index `i` is [withVariableName] + `"_${i+1}"`.
-// * Consider that monomials are sorted in lexicographic order.
-// */
-//context(NumberedPolynomialSpace<C, A>)
-//public fun <C, A: Ring<C>> NumberedPolynomial<C>.represent(withVariableName: String = NumberedPolynomial.defaultVariableName): String =
-//    coefficients.entries
-//        .sortedWith { o1, o2 -> NumberedPolynomial.monomialComparator.compare(o1.key, o2.key) }
-//        .asSequence()
-//        .map { (degs, t) ->
-//            if (degs.isEmpty()) "$t"
-//            else {
-//                when {
-//                    t.isOne() -> ""
-//                    t.isMinusOne() -> "-"
-//                    else -> "$t "
-//                } +
-//                        degs
-//                            .mapIndexed { index, deg ->
-//                                when (deg) {
-//                                    0U -> ""
-//                                    1U -> "${withVariableName}_${index+1}"
-//                                    else -> "${withVariableName}_${index+1}^$deg"
-//                                }
-//                            }
-//                            .filter { it.isNotEmpty() }
-//                            .joinToString(separator = " ") { it }
-//            }
-//        }
-//        .joinToString(separator = " + ") { it }
-//        .ifEmpty { "0" }
-//
-///**
-// * Represents the polynomial as a [String] naming variables by [namer].
-// * Consider that monomials are sorted in lexicographic order.
-// */
-//context(NumberedPolynomialSpace<C, A>)
-//public fun <C, A: Ring<C>> NumberedPolynomial<C>.represent(namer: (Int) -> String): String =
-//    coefficients.entries
-//        .sortedWith { o1, o2 -> NumberedPolynomial.monomialComparator.compare(o1.key, o2.key) }
-//        .asSequence()
-//        .map { (degs, t) ->
-//            if (degs.isEmpty()) "$t"
-//            else {
-//                when {
-//                    t.isOne() -> ""
-//                    t.isMinusOne() -> "-"
-//                    else -> "$t "
-//                } +
-//                        degs
-//                            .mapIndexed { index, deg ->
-//                                when (deg) {
-//                                    0U -> ""
-//                                    1U -> namer(index)
-//                                    else -> "${namer(index)}^$deg"
-//                                }
-//                            }
-//                            .filter { it.isNotEmpty() }
-//                            .joinToString(separator = " ") { it }
-//            }
-//        }
-//        .joinToString(separator = " + ") { it }
-//        .ifEmpty { "0" }
-//
-///**
-// * Represents the polynomial as a [String] where name of variable with index `i` is [withVariableName] + `"_${i+1}"`
-// * and with brackets around the string if needed (i.e. when there are at least two addends in the representation).
-// * Consider that monomials are sorted in lexicographic order.
-// */
-//context(NumberedPolynomialSpace<C, A>)
-//public fun <C, A: Ring<C>> NumberedPolynomial<C>.representWithBrackets(withVariableName: String = NumberedPolynomial.defaultVariableName): String =
-//    with(represent(withVariableName)) { if (coefficients.count() == 1) this else "($this)" }
-//
-///**
-// * Represents the polynomial as a [String] naming variables by [namer] and with brackets around the string if needed
-// * (i.e. when there are at least two addends in the representation).
-// * Consider that monomials are sorted in lexicographic order.
-// */
-//context(NumberedPolynomialSpace<C, A>)
-//public fun <C, A: Ring<C>> NumberedPolynomial<C>.representWithBrackets(namer: (Int) -> String): String =
-//    with(represent(namer)) { if (coefficients.count() == 1) this else "($this)" }
-//
-///**
-// * Represents the polynomial as a [String] where name of variable with index `i` is [withVariableName] + `"_${i+1}"`.
-// * Consider that monomials are sorted in **reversed** lexicographic order.
-// */
-//context(NumberedPolynomialSpace<C, A>)
-//public fun <C, A: Ring<C>> NumberedPolynomial<C>.representReversed(withVariableName: String = NumberedPolynomial.defaultVariableName): String =
-//    coefficients.entries
-//        .sortedWith { o1, o2 -> -NumberedPolynomial.monomialComparator.compare(o1.key, o2.key) }
-//        .asSequence()
-//        .map { (degs, t) ->
-//            if (degs.isEmpty()) "$t"
-//            else {
-//                when {
-//                    t.isOne() -> ""
-//                    t.isMinusOne() -> "-"
-//                    else -> "$t "
-//                } +
-//                        degs
-//                            .mapIndexed { index, deg ->
-//                                when (deg) {
-//                                    0U -> ""
-//                                    1U -> "${withVariableName}_${index+1}"
-//                                    else -> "${withVariableName}_${index+1}^$deg"
-//                                }
-//                            }
-//                            .filter { it.isNotEmpty() }
-//                            .joinToString(separator = " ") { it }
-//            }
-//        }
-//        .joinToString(separator = " + ") { it }
-//        .ifEmpty { "0" }
-//
-///**
-// * Represents the polynomial as a [String] naming variables by [namer].
-// * Consider that monomials are sorted in **reversed** lexicographic order.
-// */
-//context(NumberedPolynomialSpace<C, A>)
-//public fun <C, A: Ring<C>> NumberedPolynomial<C>.representReversed(namer: (Int) -> String): String =
-//    coefficients.entries
-//        .sortedWith { o1, o2 -> -NumberedPolynomial.monomialComparator.compare(o1.key, o2.key) }
-//        .asSequence()
-//        .map { (degs, t) ->
-//            if (degs.isEmpty()) "$t"
-//            else {
-//                when {
-//                    t.isOne() -> ""
-//                    t.isMinusOne() -> "-"
-//                    else -> "$t "
-//                } +
-//                        degs
-//                            .mapIndexed { index, deg ->
-//                                when (deg) {
-//                                    0U -> ""
-//                                    1U -> namer(index)
-//                                    else -> "${namer(index)}^$deg"
-//                                }
-//                            }
-//                            .filter { it.isNotEmpty() }
-//                            .joinToString(separator = " ") { it }
-//            }
-//        }
-//        .joinToString(separator = " + ") { it }
-//        .ifEmpty { "0" }
-//
-///**
-// * Represents the polynomial as a [String] where name of variable with index `i` is [withVariableName] + `"_${i+1}"`
-// * and with brackets around the string if needed (i.e. when there are at least two addends in the representation).
-// * Consider that monomials are sorted in **reversed** lexicographic order.
-// */
-//context(NumberedPolynomialSpace<C, A>)
-//public fun <C, A: Ring<C>> NumberedPolynomial<C>.representReversedWithBrackets(withVariableName: String = NumberedPolynomial.defaultVariableName): String =
-//    with(representReversed(withVariableName)) { if (coefficients.count() == 1) this else "($this)" }
-//
-///**
-// * Represents the polynomial as a [String] naming variables by [namer] and with brackets around the string if needed
-// * (i.e. when there are at least two addends in the representation).
-// * Consider that monomials are sorted in **reversed** lexicographic order.
-// */
-//context(NumberedPolynomialSpace<C, A>)
-//public fun <C, A: Ring<C>> NumberedPolynomial<C>.representReversedWithBrackets(namer: (Int) -> String): String =
-//    with(representReversed(namer)) { if (coefficients.count() == 1) this else "($this)" }
-
-//public fun <C> NumberedPolynomial<C>.substitute(ring: Ring<C>, args: Map<Int, C>): NumberedPolynomial<C> = ring {
-//    if (coefficients.isEmpty()) return this@substitute
-//    NumberedPolynomial<C>(
-//        buildMap {
-//            coefficients.forEach { (degs, c) ->
-//                val newDegs = degs.mapIndexed { index, deg -> if (index in args) 0U else deg }.cleanUp()
-//                val newC = degs.foldIndexed(c) { index, acc, deg ->
-//                    if (index in args) multiplyWithPower(acc, args[index]!!, deg)
-//                    else acc
-//                }
-//                this[newDegs] = if (newDegs in this) this[newDegs]!! + newC else newC
-//            }
-//        }
-//    )
-//}
-//
-//// TODO: Replace with optimisation: the [result] may be unboxed, and all operations may be performed as soon as
-////  possible on it
-//@JvmName("substitutePolynomial")
-//public fun <C> NumberedPolynomial<C>.substitute(ring: Ring<C>, arg: Map<Int, NumberedPolynomial<C>>) : NumberedPolynomial<C> =
-//    ring.numberedPolynomialSpace {
-//        if (coefficients.isEmpty()) return zero
-//        coefficients
-//            .asSequence()
-//            .map { (degs, c) ->
-//                degs.foldIndexed(
-//                    NumberedPolynomial(
-//                        degs.mapIndexed { index, deg -> if (index in arg) 0U else deg } to c
-//                    )
-//                ) { index, acc, deg -> if (index in arg) multiplyWithPower(acc, arg[index]!!, deg) else acc }
-//            }
-//            .reduce { acc, polynomial -> acc + polynomial } // TODO: Rewrite. Might be slow.
-//    }
-//
-//// TODO: Substitute rational function
-//
-//public fun <C, A : Ring<C>> NumberedPolynomial<C>.asFunctionOver(ring: A): (Map<Int, C>) -> NumberedPolynomial<C> =
-//    { substitute(ring, it) }
-//
-//public fun <C, A : Ring<C>> NumberedPolynomial<C>.asPolynomialFunctionOver(ring: A): (Map<Int, NumberedPolynomial<C>>) -> NumberedPolynomial<C> =
-//    { substitute(ring, it) }
-
-//operator fun <T: Field<T>> Polynomial<T>.div(other: T): Polynomial<T> =
-//    if (other.isZero()) throw ArithmeticException("/ by zero")
-//    else
-//        Polynomial(
-//            coefficients
-//                .mapValues { it.value / other },
-//            toCheckInput = false
-//        )
-
-/**
- * Evaluates the value of the given double polynomial for given double argument.
- */
-public fun NumberedPolynomial<Double>.substitute(args: Map<Int, Double>): NumberedPolynomial<Double> = Double.algebra {
-    val acc = LinkedHashMap<List<UInt>, Double>(coefficients.size)
-    for ((degs, c) in coefficients) {
-        val newDegs = degs.mapIndexed { index, deg -> if (index !in args) deg else 0u }.cleanUp()
-        val newC = args.entries.fold(c) { product, (variable, substitution) ->
-            val deg = degs.getOrElse(variable) { 0u }
-            if (deg == 0u) product else product * substitution.pow(deg.toInt())
-        }
-        if (newDegs !in acc) acc[newDegs] = newC
-        else acc[newDegs] = acc[newDegs]!! + newC
-    }
-    return NumberedPolynomial<Double>(acc)
-}
-
-/**
- * Evaluates the value of the given polynomial for given argument.
- *
- * It is an implementation of [Horner's method](https://en.wikipedia.org/wiki/Horner%27s_method).
- */
-public fun <C> NumberedPolynomial<C>.substitute(ring: Ring<C>, args: Map<Int, C>): NumberedPolynomial<C> = ring {
-    val acc = LinkedHashMap<List<UInt>, C>(coefficients.size)
-    for ((degs, c) in coefficients) {
-        val newDegs = degs.mapIndexed { index, deg -> if (index !in args) deg else 0u }.cleanUp()
-        val newC = args.entries.fold(c) { product, (variable, substitution) ->
-            val deg = degs.getOrElse(variable) { 0u }
-            if (deg == 0u) product else product * power(substitution, deg)
-        }
-        if (newDegs !in acc) acc[newDegs] = newC
-        else acc[newDegs] = acc[newDegs]!! + newC
-    }
-    return NumberedPolynomial<C>(acc)
-}
-
-// TODO: (Waiting for hero) Replace with optimisation: the [result] may be unboxed, and all operations may be performed
-//  as soon as possible on it
-@JvmName("substitutePolynomial")
-public fun <C> NumberedPolynomial<C>.substitute(ring: Ring<C>, args: Map<Int, NumberedPolynomial<C>>) : NumberedPolynomial<C> = TODO() /*ring.numberedPolynomial {
-    val acc = LinkedHashMap<List<UInt>, NumberedPolynomial<C>>(coefficients.size)
-    for ((degs, c) in coefficients) {
-        val newDegs = degs.mapIndexed { index, deg -> if (index !in args) deg else 0u }.cleanUp()
-        val newC = args.entries.fold(c.asNumberedPolynomial()) { product, (variable, substitution) ->
-            val deg = degs.getOrElse(variable) { 0u }
-            if (deg == 0u) product else product * power(substitution, deg)
-        }
-        if (newDegs !in acc) acc[newDegs] = c.asNumberedPolynomial()
-        else acc[newDegs] = acc[newDegs]!! + c
-    }
-}*/
-
-/**
- * Represent the polynomial as a regular context-less function.
- */
-public fun <C, A : Ring<C>> NumberedPolynomial<C>.asFunction(ring: A): (Map<Int, C>) -> NumberedPolynomial<C> = { substitute(ring, it) }
-
-/**
- * Represent the polynomial as a regular context-less function.
- */
-public fun <C, A : Ring<C>> NumberedPolynomial<C>.asPolynomialFunctionOver(ring: A): (Map<Int, NumberedPolynomial<C>>) -> NumberedPolynomial<C> = { substitute(ring, it) }
-
-/**
- * Returns algebraic derivative of received polynomial.
- */
-@UnstableKMathAPI
-public fun <C, A : Ring<C>> NumberedPolynomial<C>.derivativeWithRespectTo(
-    algebra: A,
-    variable: Int,
-): NumberedPolynomial<C> = algebra {
-    NumberedPolynomial<C>(
-        buildMap(coefficients.size) {
-            coefficients
-                .forEach { (degs, c) ->
-                    if (degs.size > variable) return@forEach
-                    put(
-                        degs.mapIndexed { index, deg ->
-                            when {
-                                index != variable -> deg
-                                deg > 0u -> deg - 1u
-                                else -> return@forEach
-                            }
-                        }.cleanUp(),
-                        multiplyByDoubling(c, degs[variable])
-                    )
-                }
-        }
-    )
-}
-
-/**
- * Returns algebraic derivative of received polynomial.
- */
-@UnstableKMathAPI
-public fun <C, A : Ring<C>> NumberedPolynomial<C>.derivativeWithRespectTo(
-    algebra: A,
-    variables: Collection<Int>,
-): NumberedPolynomial<C> = algebra {
-    val cleanedVariables = variables.toSet()
-    if (cleanedVariables.isEmpty()) return this@derivativeWithRespectTo
-    val maxRespectedVariable = cleanedVariables.maxOrNull()!!
-    NumberedPolynomial<C>(
-        buildMap(coefficients.size) {
-            coefficients
-                .forEach { (degs, c) ->
-                    if (degs.size > maxRespectedVariable) return@forEach
-                    put(
-                        degs.mapIndexed { index, deg ->
-                            when {
-                                index !in cleanedVariables -> deg
-                                deg > 0u -> deg - 1u
-                                else -> return@forEach
-                            }
-                        }.cleanUp(),
-                        cleanedVariables.fold(c) { acc, variable -> multiplyByDoubling(acc, degs[variable]) }
-                    )
-                }
-        }
-    )
-}
-
-/**
- * Returns algebraic derivative of received polynomial.
- */
-@UnstableKMathAPI
-public fun <C, A : Ring<C>> NumberedPolynomial<C>.nthDerivativeWithRespectTo(
-    algebra: A,
-    variable: Int,
-    order: UInt
-): NumberedPolynomial<C> = algebra {
-    if (order == 0u) return this@nthDerivativeWithRespectTo
-    NumberedPolynomial<C>(
-        buildMap(coefficients.size) {
-            coefficients
-                .forEach { (degs, c) ->
-                    if (degs.size > variable) return@forEach
-                    put(
-                        degs.mapIndexed { index, deg ->
-                            when {
-                                index != variable -> deg
-                                deg >= order -> deg - order
-                                else -> return@forEach
-                            }
-                        }.cleanUp(),
-                        degs[variable].let { deg ->
-                            (deg downTo deg - order + 1u)
-                                .fold(c) { acc, ord -> multiplyByDoubling(acc, ord) }
-                        }
-                    )
-                }
-        }
-    )
-}
-
-/**
- * Returns algebraic derivative of received polynomial.
- */
-@UnstableKMathAPI
-public fun <C, A : Ring<C>> NumberedPolynomial<C>.nthDerivativeWithRespectTo(
-    algebra: A,
-    variablesAndOrders: Map<Int, UInt>,
-): NumberedPolynomial<C> = algebra {
-    val filteredVariablesAndOrders = variablesAndOrders.filterValues { it != 0u }
-    if (filteredVariablesAndOrders.isEmpty()) return this@nthDerivativeWithRespectTo
-    val maxRespectedVariable = filteredVariablesAndOrders.keys.maxOrNull()!!
-    NumberedPolynomial<C>(
-        buildMap(coefficients.size) {
-            coefficients
-                .forEach { (degs, c) ->
-                    if (degs.size > maxRespectedVariable) return@forEach
-                    put(
-                        degs.mapIndexed { index, deg ->
-                            if (index !in filteredVariablesAndOrders) return@mapIndexed deg
-                            val order = filteredVariablesAndOrders[index]!!
-                            if (deg >= order) deg - order else return@forEach
-                        }.cleanUp(),
-                        filteredVariablesAndOrders.entries.fold(c) { acc1, (index, order) ->
-                            degs[index].let { deg ->
-                                (deg downTo deg - order + 1u)
-                                    .fold(acc1) { acc2, ord -> multiplyByDoubling(acc2, ord) }
-                            }
-                        }
-                    )
-                }
-        }
-    )
-}
-
-/**
- * Returns algebraic antiderivative of received polynomial.
- */
-@UnstableKMathAPI
-public fun <C, A : Field<C>> NumberedPolynomial<C>.antiderivativeWithRespectTo(
-    algebra: A,
-    variable: Int,
-): NumberedPolynomial<C> = algebra {
-    NumberedPolynomial<C>(
-        buildMap(coefficients.size) {
-            coefficients
-                .forEach { (degs, c) ->
-                    put(
-                        List(max(variable + 1, degs.size)) { if (it != variable) degs[it] else degs[it] + 1u },
-                        c / multiplyByDoubling(one, degs[variable])
-                    )
-                }
-        }
-    )
-}
-
-/**
- * Returns algebraic antiderivative of received polynomial.
- */
-@UnstableKMathAPI
-public fun <C, A : Field<C>> NumberedPolynomial<C>.antiderivativeWithRespectTo(
-    algebra: A,
-    variables: Collection<Int>,
-): NumberedPolynomial<C> = algebra {
-    val cleanedVariables = variables.toSet()
-    if (cleanedVariables.isEmpty()) return this@antiderivativeWithRespectTo
-    val maxRespectedVariable = cleanedVariables.maxOrNull()!!
-    NumberedPolynomial<C>(
-        buildMap(coefficients.size) {
-            coefficients
-                .forEach { (degs, c) ->
-                    put(
-                        List(max(maxRespectedVariable + 1, degs.size)) { if (it !in variables) degs[it] else degs[it] + 1u },
-                        cleanedVariables.fold(c) { acc, variable -> acc / multiplyByDoubling(one, degs[variable]) }
-                    )
-                }
-        }
-    )
-}
-
-/**
- * Returns algebraic derivative of received polynomial.
- */
-@UnstableKMathAPI
-public fun <C, A : Field<C>> NumberedPolynomial<C>.nthAntiderivativeWithRespectTo(
-    algebra: A,
-    variable: Int,
-    order: UInt
-): NumberedPolynomial<C> = algebra {
-    if (order == 0u) return this@nthAntiderivativeWithRespectTo
-    NumberedPolynomial<C>(
-        buildMap(coefficients.size) {
-            coefficients
-                .forEach { (degs, c) ->
-                    put(
-                        List(max(variable + 1, degs.size)) { if (it != variable) degs[it] else degs[it] + order },
-                        degs[variable].let { deg ->
-                            (deg downTo deg - order + 1u)
-                                .fold(c) { acc, ord -> acc / multiplyByDoubling(one, ord) }
-                        }
-                    )
-                }
-        }
-    )
-}
-
-/**
- * Returns algebraic derivative of received polynomial.
- */
-@UnstableKMathAPI
-public fun <C, A : Field<C>> NumberedPolynomial<C>.nthAntiderivativeWithRespectTo(
-    algebra: A,
-    variablesAndOrders: Map<Int, UInt>,
-): NumberedPolynomial<C> = algebra {
-    val filteredVariablesAndOrders = variablesAndOrders.filterValues { it != 0u }
-    if (filteredVariablesAndOrders.isEmpty()) return this@nthAntiderivativeWithRespectTo
-    val maxRespectedVariable = filteredVariablesAndOrders.keys.maxOrNull()!!
-    NumberedPolynomial<C>(
-        buildMap(coefficients.size) {
-            coefficients
-                .forEach { (degs, c) ->
-                    put(
-                        List(max(maxRespectedVariable + 1, degs.size)) { degs[it] + filteredVariablesAndOrders.getOrElse(it) { 0u } },
-                        filteredVariablesAndOrders.entries.fold(c) { acc1, (index, order) ->
-                            degs[index].let { deg ->
-                                (deg downTo deg - order + 1u)
-                                    .fold(acc1) { acc2, ord -> acc2 / multiplyByDoubling(one, ord) }
-                            }
-                        }
-                    )
-                }
-        }
-    )
-}

kmath-functions/src/commonMain/kotlin/space/kscience/kmath/functions/numberedRationalFunctionUtil.kt

@@ -1,33 +0,0 @@
-/*
- * Copyright 2018-2021 KMath contributors.
- * Use of this source code is governed by the Apache 2.0 license that can be found in the license/LICENSE.txt file.
- */
-
-package space.kscience.kmath.functions
-
-import space.kscience.kmath.operations.Ring
-import kotlin.contracts.InvocationKind
-import kotlin.contracts.contract
-
-
-/**
- * Creates a [NumberedRationalFunctionSpace] over a received ring.
- */
-public fun <C, A : Ring<C>> A.numberedRationalFunction(): NumberedRationalFunctionSpace<C, A> =
-    NumberedRationalFunctionSpace(this)
-
-/**
- * Creates a [NumberedRationalFunctionSpace]'s scope over a received ring.
- */
-public inline fun <C, A : Ring<C>, R> A.numberedRationalFunction(block: NumberedRationalFunctionSpace<C, A>.() -> R): R {
-    contract { callsInPlace(block, InvocationKind.EXACTLY_ONCE) }
-    return NumberedRationalFunctionSpace(this).block()
-}
-
-//fun <T: Field<T>> NumberedRationalFunction<T>.reduced(): NumberedRationalFunction<T> {
-//    val greatestCommonDivider = polynomialGCD(numerator, denominator)
-//    return NumberedRationalFunction(
-//        numerator / greatestCommonDivider,
-//        denominator / greatestCommonDivider
-//    )
-//}

kmath-functions/src/commonMain/kotlin/space/kscience/kmath/functions/numberedUtil.kt

@@ -0,0 +1,513 @@
+/*
+ * Copyright 2018-2021 KMath contributors.
+ * Use of this source code is governed by the Apache 2.0 license that can be found in the license/LICENSE.txt file.
+ */
+
+package space.kscience.kmath.functions
+
+import space.kscience.kmath.misc.UnstableKMathAPI
+import space.kscience.kmath.operations.Field
+import space.kscience.kmath.operations.Ring
+import space.kscience.kmath.operations.algebra
+import space.kscience.kmath.operations.invoke
+import space.kscience.kmath.structures.Buffer
+import kotlin.contracts.InvocationKind
+import kotlin.contracts.contract
+import kotlin.jvm.JvmName
+import kotlin.math.max
+import kotlin.math.min
+
+
+/**
+ * Creates a [NumberedPolynomialSpace] over a received ring.
+ */
+public fun <C, A : Ring<C>> A.numberedPolynomialSpace(): NumberedPolynomialSpace<C, A> =
+    NumberedPolynomialSpace(this)
+
+/**
+ * Creates a [NumberedPolynomialSpace]'s scope over a received ring.
+ */
+public inline fun <C, A : Ring<C>, R> A.numberedPolynomialSpace(block: NumberedPolynomialSpace<C, A>.() -> R): R {
+    contract { callsInPlace(block, InvocationKind.EXACTLY_ONCE) }
+    return NumberedPolynomialSpace(this).block()
+}
+
+/**
+ * Creates a [NumberedRationalFunctionSpace] over a received ring.
+ */
+public fun <C, A : Ring<C>> A.numberedRationalFunctionSpace(): NumberedRationalFunctionSpace<C, A> =
+    NumberedRationalFunctionSpace(this)
+
+/**
+ * Creates a [NumberedRationalFunctionSpace]'s scope over a received ring.
+ */
+public inline fun <C, A : Ring<C>, R> A.numberedRationalFunctionSpace(block: NumberedRationalFunctionSpace<C, A>.() -> R): R {
+    contract { callsInPlace(block, InvocationKind.EXACTLY_ONCE) }
+    return NumberedRationalFunctionSpace(this).block()
+}
+
+/**
+ * Substitutes provided Double arguments [args] into [this] Double polynomial.
+ */
+public fun NumberedPolynomial<Double>.substitute(args: Map<Int, Double>): NumberedPolynomial<Double> = Double.algebra {
+    NumberedPolynomial<Double>(
+        buildMap(coefficients.size) {
+            for ((degs, c) in coefficients) {
+                val newDegs = degs.mapIndexed { index, deg -> if (index !in args) deg else 0u }.cleanUp()
+                val newC = args.entries.fold(c) { product, (variable, substitution) ->
+                    val deg = degs.getOrElse(variable) { 0u }
+                    if (deg == 0u) product else product * substitution.pow(deg.toInt())
+                }
+                this[newDegs] = if (newDegs !in this) newC else this[newDegs]!! + newC
+            }
+        }
+    )
+}
+
+/**
+ * Substitutes provided arguments [args] into [this] polynomial.
+ */
+public fun <C> NumberedPolynomial<C>.substitute(ring: Ring<C>, args: Map<Int, C>): NumberedPolynomial<C> = ring {
+    NumberedPolynomial<C>(
+        buildMap(coefficients.size) {
+            for ((degs, c) in coefficients) {
+                val newDegs = degs.mapIndexed { index, deg -> if (index !in args) deg else 0u }.cleanUp()
+                val newC = args.entries.fold(c) { product, (variable, substitution) ->
+                    val deg = degs.getOrElse(variable) { 0u }
+                    if (deg == 0u) product else product * power(substitution, deg)
+                }
+                this[newDegs] = if (newDegs !in this) newC else this[newDegs]!! + newC
+            }
+        }
+    )
+}
+
+/**
+ * Substitutes provided arguments [args] into [this] polynomial.
+ */ // TODO: To optimize boxing
+@JvmName("substitutePolynomial")
+public fun <C> NumberedPolynomial<C>.substitute(ring: Ring<C>, args: Map<Int, NumberedPolynomial<C>>) : NumberedPolynomial<C> =
+    ring.numberedPolynomialSpace {
+        coefficients.entries.fold(zero) { acc, (degs, c) ->
+            val newDegs = degs.mapIndexed { index, deg -> if (index !in args) deg else 0u }.cleanUp()
+            acc + args.entries.fold(NumberedPolynomial<C>(mapOf(newDegs to c))) { product, (variable, substitution) ->
+                val deg = degs.getOrElse(variable) { 0u }
+                if (deg == 0u) product else product * power(substitution, deg)
+            }
+        }
+    }
+
+/**
+ * Substitutes provided arguments [args] into [this] polynomial.
+ */ // TODO: To optimize boxing
+@JvmName("substituteRationalFunction")
+public fun <C> NumberedPolynomial<C>.substitute(ring: Ring<C>, args: Map<Int, NumberedRationalFunction<C>>) : NumberedRationalFunction<C> =
+    ring.numberedRationalFunctionSpace {
+        coefficients.entries.fold(zero) { acc, (degs, c) ->
+            val newDegs = degs.mapIndexed { index, deg -> if (index !in args) deg else 0u }.cleanUp()
+            acc + args.entries.fold(NumberedRationalFunction(NumberedPolynomial<C>(mapOf(newDegs to c)))) { product, (variable, substitution) ->
+                val deg = degs.getOrElse(variable) { 0u }
+                if (deg == 0u) product else product * power(substitution, deg)
+            }
+        }
+    }
+
+/**
+ * Substitutes provided Double arguments [args] into [this] Double rational function.
+ */
+public fun NumberedRationalFunction<Double>.substitute(args: Map<Int, Double>): NumberedRationalFunction<Double> =
+    NumberedRationalFunction(numerator.substitute(args), denominator.substitute(args))
+
+/**
+ * Substitutes provided arguments [args] into [this] rational function.
+ */
+public fun <C> NumberedRationalFunction<C>.substitute(ring: Ring<C>, args: Map<Int, C>): NumberedRationalFunction<C> =
+    NumberedRationalFunction(numerator.substitute(ring, args), denominator.substitute(ring, args))
+
+/**
+ * Substitutes provided arguments [args] into [this] rational function.
+ */ // TODO: To optimize calculation
+@JvmName("substitutePolynomial")
+public fun <C> NumberedRationalFunction<C>.substitute(ring: Ring<C>, args: Map<Int, NumberedPolynomial<C>>) : NumberedRationalFunction<C> =
+    NumberedRationalFunction(numerator.substitute(ring, args), denominator.substitute(ring, args))
+
+/**
+ * Substitutes provided arguments [args] into [this] rational function.
+ */ // TODO: To optimize calculation
+@JvmName("substituteRationalFunction")
+public fun <C> NumberedRationalFunction<C>.substitute(ring: Ring<C>, args: Map<Int, NumberedRationalFunction<C>>) : NumberedRationalFunction<C> =
+    ring.numberedRationalFunctionSpace {
+        numerator.substitute(ring, args) / denominator.substitute(ring, args)
+    }
+
+/**
+ * Substitutes provided Double arguments [args] into [this] Double polynomial.
+ */
+public fun NumberedPolynomial<Double>.substitute(args: Buffer<Double>): NumberedPolynomial<Double> = Double.algebra {
+    val lastSubstitutionVariable = args.size - 1
+    NumberedPolynomial<Double>(
+        buildMap(coefficients.size) {
+            for ((degs, c) in coefficients) {
+                val lastDegsIndex = degs.lastIndex
+                val newDegs =
+                    if (lastDegsIndex <= lastSubstitutionVariable) emptyList()
+                    else degs.toMutableList().apply {
+                        for (i in 0..lastSubstitutionVariable) this[i] = 0u
+                    }
+                val newC = (0..min(lastDegsIndex, lastSubstitutionVariable)).fold(c) { product, variable ->
+                    val deg = degs[variable]
+                    if (deg == 0u) product else product * args[variable].pow(deg.toInt())
+                }
+                if (newDegs !in this) this[newDegs] = newC
+                else this[newDegs] = this[newDegs]!! + newC
+            }
+        }
+    )
+}
+
+/**
+ * Substitutes provided arguments [args] into [this] polynomial.
+ */
+public fun <C> NumberedPolynomial<C>.substitute(ring: Ring<C>, args: Buffer<C>): NumberedPolynomial<C> = ring {
+    val lastSubstitutionVariable = args.size - 1
+    NumberedPolynomial<C>(
+        buildMap<List<UInt>, C>(coefficients.size) {
+            for ((degs, c) in coefficients) {
+                val lastDegsIndex = degs.lastIndex
+                val newDegs =
+                    if (lastDegsIndex <= lastSubstitutionVariable) emptyList()
+                    else degs.toMutableList().apply {
+                        for (i in 0..lastSubstitutionVariable) this[i] = 0u
+                    }
+                val newC = (0..min(lastDegsIndex, lastSubstitutionVariable)).fold(c) { product, variable ->
+                    val deg = degs[variable]
+                    if (deg == 0u) product else product * power(args[variable], deg)
+                }
+                if (newDegs !in this) this[newDegs] = newC
+                else this[newDegs] = this[newDegs]!! + newC
+            }
+        }
+    )
+}
+
+/**
+ * Substitutes provided arguments [args] into [this] polynomial.
+ */ // TODO: To optimize boxing
+@JvmName("substitutePolynomial")
+public fun <C> NumberedPolynomial<C>.substitute(ring: Ring<C>, args: Buffer<NumberedPolynomial<C>>) : NumberedPolynomial<C> =
+    ring.numberedPolynomialSpace {
+        val lastSubstitutionVariable = args.size - 1
+        coefficients.entries.fold(zero) { acc, (degs, c) ->
+            val lastDegsIndex = degs.lastIndex
+            val newDegs =
+                if (lastDegsIndex <= lastSubstitutionVariable) emptyList()
+                else degs.toMutableList().apply {
+                    for (i in 0..lastSubstitutionVariable) this[i] = 0u
+                }
+            acc + (0..min(lastDegsIndex, lastSubstitutionVariable))
+                .fold(NumberedPolynomial<C>(mapOf(newDegs to c))) { product, variable ->
+                    val deg = degs[variable]
+                    if (deg == 0u) product else product * power(args[variable], deg)
+                }
+        }
+    }
+
+/**
+ * Substitutes provided arguments [args] into [this] polynomial.
+ */ // TODO: To optimize boxing
+@JvmName("substituteRationalFunction")
+public fun <C> NumberedPolynomial<C>.substitute(ring: Ring<C>, args: Buffer<NumberedRationalFunction<C>>) : NumberedRationalFunction<C> =
+    ring.numberedRationalFunctionSpace {
+        val lastSubstitutionVariable = args.size - 1
+        coefficients.entries.fold(zero) { acc, (degs, c) ->
+            val lastDegsIndex = degs.lastIndex
+            val newDegs =
+                if (lastDegsIndex <= lastSubstitutionVariable) emptyList()
+                else degs.toMutableList().apply {
+                    for (i in 0..lastSubstitutionVariable) this[i] = 0u
+                }
+            acc + (0..min(lastDegsIndex, lastSubstitutionVariable))
+                .fold(NumberedRationalFunction(NumberedPolynomial<C>(mapOf(newDegs to c)))) { product, variable ->
+                    val deg = degs[variable]
+                    if (deg == 0u) product else product * power(args[variable], deg)
+                }
+        }
+    }
+
+/**
+ * Substitutes provided Double arguments [args] into [this] Double rational function.
+ */
+public fun NumberedRationalFunction<Double>.substitute(args: Buffer<Double>): NumberedRationalFunction<Double> =
+    NumberedRationalFunction(numerator.substitute(args), denominator.substitute(args))
+
+/**
+ * Substitutes provided arguments [args] into [this] rational function.
+ */
+public fun <C> NumberedRationalFunction<C>.substitute(ring: Ring<C>, args: Buffer<C>): NumberedRationalFunction<C> =
+    NumberedRationalFunction(numerator.substitute(ring, args), denominator.substitute(ring, args))
+
+/**
+ * Substitutes provided arguments [args] into [this] rational function.
+ */ // TODO: To optimize calculation
+@JvmName("substitutePolynomial")
+public fun <C> NumberedRationalFunction<C>.substitute(ring: Ring<C>, args: Buffer<NumberedPolynomial<C>>) : NumberedRationalFunction<C> =
+    NumberedRationalFunction(numerator.substitute(ring, args), denominator.substitute(ring, args))
+
+/**
+ * Substitutes provided arguments [args] into [this] rational function.
+ */ // TODO: To optimize calculation
+@JvmName("substituteRationalFunction")
+public fun <C> NumberedRationalFunction<C>.substitute(ring: Ring<C>, args: Buffer<NumberedRationalFunction<C>>) : NumberedRationalFunction<C> =
+    ring.numberedRationalFunctionSpace {
+        numerator.substitute(ring, args) / denominator.substitute(ring, args)
+    }
+
+/**
+ * Substitutes provided Double arguments [args] into [this] Double polynomial.
+ */
+public fun NumberedPolynomial<Double>.substituteFully(args: Buffer<Double>): Double = Double.algebra {
+    val lastSubstitutionVariable = args.size - 1
+    require(coefficients.keys.all { it.lastIndex <= lastSubstitutionVariable }) { "Fully substituting buffer should cover all variables of the polynomial." }
+    coefficients.entries.fold(.0) { acc, (degs, c) ->
+        acc + degs.foldIndexed(c) { variable, product, deg ->
+            if (deg == 0u) product else product * args[variable].pow(deg.toInt())
+        }
+    }
+}
+
+/**
+ * Substitutes provided arguments [args] into [this] polynomial.
+ */
+public fun <C> NumberedPolynomial<C>.substituteFully(ring: Ring<C>, args: Buffer<C>): C = ring {
+    val lastSubstitutionVariable = args.size - 1
+    require(coefficients.keys.all { it.lastIndex <= lastSubstitutionVariable }) { "Fully substituting buffer should cover all variables of the polynomial." }
+    coefficients.entries.fold(zero) { acc, (degs, c) ->
+        acc + degs.foldIndexed(c) { variable, product, deg ->
+            if (deg == 0u) product else product * power(args[variable], deg)
+        }
+    }
+}
+
+/**
+ * Substitutes provided Double arguments [args] into [this] Double rational function.
+ */
+public fun NumberedRationalFunction<Double>.substituteFully(args: Buffer<Double>): Double =
+    numerator.substituteFully(args) / denominator.substituteFully(args)
+
+/**
+ * Substitutes provided arguments [args] into [this] rational function.
+ */
+public fun <C> NumberedRationalFunction<C>.substituteFully(ring: Field<C>, args: Buffer<C>): C = ring {
+    numerator.substituteFully(ring, args) / denominator.substituteFully(ring, args)
+}
+
+/**
+ * Represent [this] polynomial as a regular context-less function.
+ */
+public fun <C, A : Ring<C>> NumberedPolynomial<C>.asFunctionOver(ring: A): (Buffer<C>) -> C = { substituteFully(ring, it) }
+
+/**
+ * Represent [this] polynomial as a regular context-less function.
+ */
+public fun <C, A : Ring<C>> NumberedPolynomial<C>.asFunctionOfConstantOver(ring: A): (Buffer<C>) -> C = { substituteFully(ring, it) }
+
+/**
+ * Represent [this] polynomial as a regular context-less function.
+ */
+public fun <C, A : Ring<C>> NumberedPolynomial<C>.asFunctionOfPolynomialOver(ring: A): (Buffer<NumberedPolynomial<C>>) -> NumberedPolynomial<C> = { substitute(ring, it) }
+
+/**
+ * Represent [this] polynomial as a regular context-less function.
+ */
+public fun <C, A : Ring<C>> NumberedPolynomial<C>.asFunctionOfRationalFunctionOver(ring: A): (Buffer<NumberedRationalFunction<C>>) -> NumberedRationalFunction<C> = { substitute(ring, it) }
+
+/**
+ * Represent [this] rational function as a regular context-less function.
+ */
+public fun <C, A : Field<C>> NumberedRationalFunction<C>.asFunctionOver(ring: A): (Buffer<C>) -> C = { substituteFully(ring, it) }
+
+/**
+ * Represent [this] rational function as a regular context-less function.
+ */
+public fun <C, A : Field<C>> NumberedRationalFunction<C>.asFunctionOfConstantOver(ring: A): (Buffer<C>) -> C = { substituteFully(ring, it) }
+
+/**
+ * Represent [this] rational function as a regular context-less function.
+ */
+public fun <C, A : Ring<C>> NumberedRationalFunction<C>.asFunctionOfPolynomialOver(ring: A): (Buffer<NumberedPolynomial<C>>) -> NumberedRationalFunction<C> = { substitute(ring, it) }
+
+/**
+ * Represent [this] rational function as a regular context-less function.
+ */
+public fun <C, A : Ring<C>> NumberedRationalFunction<C>.asFunctionOfRationalFunctionOver(ring: A): (Buffer<NumberedRationalFunction<C>>) -> NumberedRationalFunction<C> = { substitute(ring, it) }
+
+/**
+ * Returns algebraic derivative of received polynomial with respect to provided variable.
+ */
+@UnstableKMathAPI
+public fun <C, A : Ring<C>> NumberedPolynomial<C>.derivativeWithRespectTo(
+    ring: A,
+    variable: Int,
+): NumberedPolynomial<C> = ring {
+    NumberedPolynomial<C>(
+        buildMap(coefficients.size) {
+            coefficients
+                .forEach { (degs, c) ->
+                    if (degs.size > variable) return@forEach
+                    put(
+                        degs.mapIndexed { index, deg ->
+                            when {
+                                index != variable -> deg
+                                deg > 0u -> deg - 1u
+                                else -> return@forEach
+                            }
+                        }.cleanUp(),
+                        multiplyByDoubling(c, degs[variable])
+                    )
+                }
+        }
+    )
+}
+
+/**
+ * Returns algebraic derivative of received polynomial with respect to provided variable of specified order.
+ */
+@UnstableKMathAPI
+public fun <C, A : Ring<C>> NumberedPolynomial<C>.nthDerivativeWithRespectTo(
+    ring: A,
+    variable: Int,
+    order: UInt
+): NumberedPolynomial<C> = ring {
+    if (order == 0u) return this@nthDerivativeWithRespectTo
+    NumberedPolynomial<C>(
+        buildMap(coefficients.size) {
+            coefficients
+                .forEach { (degs, c) ->
+                    if (degs.size > variable) return@forEach
+                    put(
+                        degs.mapIndexed { index, deg ->
+                            when {
+                                index != variable -> deg
+                                deg >= order -> deg - order
+                                else -> return@forEach
+                            }
+                        }.cleanUp(),
+                        degs[variable].let { deg ->
+                            (deg downTo deg - order + 1u)
+                                .fold(c) { acc, ord -> multiplyByDoubling(acc, ord) }
+                        }
+                    )
+                }
+        }
+    )
+}
+
+/**
+ * Returns algebraic derivative of received polynomial with respect to provided variables of specified orders.
+ */
+@UnstableKMathAPI
+public fun <C, A : Ring<C>> NumberedPolynomial<C>.nthDerivativeWithRespectTo(
+    ring: A,
+    variablesAndOrders: Map<Int, UInt>,
+): NumberedPolynomial<C> = ring {
+    val filteredVariablesAndOrders = variablesAndOrders.filterValues { it != 0u }
+    if (filteredVariablesAndOrders.isEmpty()) return this@nthDerivativeWithRespectTo
+    val maxRespectedVariable = filteredVariablesAndOrders.keys.maxOrNull()!!
+    NumberedPolynomial<C>(
+        buildMap(coefficients.size) {
+            coefficients
+                .forEach { (degs, c) ->
+                    if (degs.size > maxRespectedVariable) return@forEach
+                    put(
+                        degs.mapIndexed { index, deg ->
+                            if (index !in filteredVariablesAndOrders) return@mapIndexed deg
+                            val order = filteredVariablesAndOrders[index]!!
+                            if (deg >= order) deg - order else return@forEach
+                        }.cleanUp(),
+                        filteredVariablesAndOrders.entries.fold(c) { acc1, (index, order) ->
+                            degs[index].let { deg ->
+                                (deg downTo deg - order + 1u)
+                                    .fold(acc1) { acc2, ord -> multiplyByDoubling(acc2, ord) }
+                            }
+                        }
+                    )
+                }
+        }
+    )
+}
+
+/**
+ * Returns algebraic antiderivative of received polynomial with respect to provided variable.
+ */
+@UnstableKMathAPI
+public fun <C, A : Field<C>> NumberedPolynomial<C>.antiderivativeWithRespectTo(
+    ring: A,
+    variable: Int,
+): NumberedPolynomial<C> = ring {
+    NumberedPolynomial<C>(
+        buildMap(coefficients.size) {
+            coefficients
+                .forEach { (degs, c) ->
+                    put(
+                        List(max(variable + 1, degs.size)) { if (it != variable) degs[it] else degs[it] + 1u },
+                        c / multiplyByDoubling(one, degs[variable])
+                    )
+                }
+        }
+    )
+}
+
+/**
+ * Returns algebraic antiderivative of received polynomial with respect to provided variable of specified order.
+ */
+@UnstableKMathAPI
+public fun <C, A : Field<C>> NumberedPolynomial<C>.nthAntiderivativeWithRespectTo(
+    ring: A,
+    variable: Int,
+    order: UInt
+): NumberedPolynomial<C> = ring {
+    if (order == 0u) return this@nthAntiderivativeWithRespectTo
+    NumberedPolynomial<C>(
+        buildMap(coefficients.size) {
+            coefficients
+                .forEach { (degs, c) ->
+                    put(
+                        List(max(variable + 1, degs.size)) { if (it != variable) degs[it] else degs[it] + order },
+                        degs[variable].let { deg ->
+                            (deg downTo deg - order + 1u)
+                                .fold(c) { acc, ord -> acc / multiplyByDoubling(one, ord) }
+                        }
+                    )
+                }
+        }
+    )
+}
+
+/**
+ * Returns algebraic derivative of received polynomial with respect to provided variables of specified orders.
+ */
+@UnstableKMathAPI
+public fun <C, A : Field<C>> NumberedPolynomial<C>.nthAntiderivativeWithRespectTo(
+    ring: A,
+    variablesAndOrders: Map<Int, UInt>,
+): NumberedPolynomial<C> = ring {
+    val filteredVariablesAndOrders = variablesAndOrders.filterValues { it != 0u }
+    if (filteredVariablesAndOrders.isEmpty()) return this@nthAntiderivativeWithRespectTo
+    val maxRespectedVariable = filteredVariablesAndOrders.keys.maxOrNull()!!
+    NumberedPolynomial<C>(
+        buildMap(coefficients.size) {
+            coefficients
+                .forEach { (degs, c) ->
+                    put(
+                        List(max(maxRespectedVariable + 1, degs.size)) { degs[it] + filteredVariablesAndOrders.getOrElse(it) { 0u } },
+                        filteredVariablesAndOrders.entries.fold(c) { acc1, (index, order) ->
+                            degs[index].let { deg ->
+                                (deg downTo deg - order + 1u)
+                                    .fold(acc1) { acc2, ord -> acc2 / multiplyByDoubling(one, ord) }
+                            }
+                        }
+                    )
+                }
+        }
+    )
+}

kmath-functions/src/commonTest/kotlin/space/kscience/kmath/functions/ListPolynomialTest.kt

@@ -3,6 +3,8 @@
  * Use of this source code is governed by the Apache 2.0 license that can be found in the license/LICENSE.txt file.
  */
 
+@file:Suppress("LocalVariableName")
+
 package space.kscience.kmath.functions
 
 import space.kscience.kmath.test.misc.*
@@ -12,7 +14,7 @@ import kotlin.test.*
 class ListPolynomialTest {
     @Test
     fun test_Polynomial_Int_plus() {
-        RationalField.listPolynomial {
+        RationalField.listPolynomialSpace {
             assertEquals(
                 ListPolynomial(Rational(-22, 9), Rational(-8, 9), Rational(-8, 7)),
                 ListPolynomial(Rational(5, 9), Rational(-8, 9), Rational(-8, 7)) + -3,
@@ -28,31 +30,38 @@ class ListPolynomialTest {
                 ListPolynomial(Rational(-2)) + 2,
                 "test 3"
             )
-            assertEquals(
-                ListPolynomial(),
-                ListPolynomial<Rational>() + 0,
+            val polynomial_4 = ListPolynomial<Rational>()
+            assertSame(
+                polynomial_4,
+                polynomial_4 + 0,
                 "test 4"
             )
+            val polynomial_5 = ListPolynomial(Rational(-22, 9), Rational(-8, 9), Rational(-8, 7))
+            assertSame(
+                polynomial_5,
+                polynomial_5 + 0,
+                "test 5"
+            )
             assertEquals(
                 ListPolynomial(Rational(-1), Rational(0), Rational(0), Rational(0)),
                 ListPolynomial(Rational(-2), Rational(0), Rational(0), Rational(0)) + 1,
-                "test 5"
+                "test 6"
             )
             assertEquals(
                 ListPolynomial(Rational(-1)),
                 ListPolynomial(Rational(-2)) + 1,
-                "test 6"
+                "test 7"
             )
             assertEquals(
                 ListPolynomial(Rational(2)),
                 ListPolynomial<Rational>() + 2,
-                "test 7"
+                "test 8"
             )
         }
     }
     @Test
     fun test_Polynomial_Int_minus() {
-        RationalField.listPolynomial {
+        RationalField.listPolynomialSpace {
             assertEquals(
                 ListPolynomial(Rational(32, 9), Rational(-8, 9), Rational(-8, 7)),
                 ListPolynomial(Rational(5, 9), Rational(-8, 9), Rational(-8, 7)) - -3,
@@ -68,31 +77,38 @@ class ListPolynomialTest {
                 ListPolynomial(Rational(2)) - 2,
                 "test 3"
             )
-            assertEquals(
-                ListPolynomial(),
-                ListPolynomial<Rational>() - 0,
+            val polynomial_4 = ListPolynomial<Rational>()
+            assertSame(
+                polynomial_4,
+                polynomial_4 - 0,
                 "test 4"
             )
+            val polynomial_5 = ListPolynomial(Rational(-22, 9), Rational(-8, 9), Rational(-8, 7))
+            assertEquals(
+                polynomial_5,
+                polynomial_5 - 0,
+                "test 5"
+            )
             assertEquals(
                 ListPolynomial(Rational(1), Rational(0), Rational(0), Rational(0)),
                 ListPolynomial(Rational(2), Rational(0), Rational(0), Rational(0)) - 1,
-                "test 5"
+                "test 6"
             )
             assertEquals(
                 ListPolynomial(Rational(1)),
                 ListPolynomial(Rational(2)) - 1,
-                "test 6"
+                "test 7"
             )
             assertEquals(
                 ListPolynomial(Rational(-2)),
                 ListPolynomial<Rational>() - 2,
-                "test 7"
+                "test 8"
             )
         }
     }
     @Test
     fun test_Polynomial_Int_times() {
-        IntModuloRing(35).listPolynomial {
+        IntModuloRing(35).listPolynomialSpace {
             assertEquals(
                 ListPolynomial(34, 2, 1, 20, 2),
                 ListPolynomial(22, 26, 13, 15, 26) * 27,
@@ -103,11 +119,22 @@ class ListPolynomialTest {
                 ListPolynomial(7, 0, 49, 21, 14) * 15,
                 "test 2"
             )
+            val polynomial = ListPolynomial(22, 26, 13, 15, 26)
+            assertSame(
+                zero,
+                polynomial * 0,
+                "test 3"
+            )
+            assertSame(
+                polynomial,
+                polynomial * 1,
+                "test 4"
+            )
         }
     }
     @Test
     fun test_Int_Polynomial_plus() {
-        RationalField.listPolynomial {
+        RationalField.listPolynomialSpace {
             assertEquals(
                 ListPolynomial(Rational(-22, 9), Rational(-8, 9), Rational(-8, 7)),
                 -3 + ListPolynomial(Rational(5, 9), Rational(-8, 9), Rational(-8, 7)),
@@ -123,31 +150,38 @@ class ListPolynomialTest {
                 2 + ListPolynomial(Rational(-2)),
                 "test 3"
             )
-            assertEquals(
-                ListPolynomial(),
-                0 + ListPolynomial(),
+            val polynomial_4 = ListPolynomial<Rational>()
+            assertSame(
+                polynomial_4,
+                0 + polynomial_4,
                 "test 4"
             )
+            val polynomial_5 = ListPolynomial<Rational>(Rational(-22, 9), Rational(-8, 9), Rational(-8, 7))
+            assertSame(
+                polynomial_5,
+                0 + polynomial_5,
+                "test 5"
+            )
             assertEquals(
                 ListPolynomial(Rational(-1), Rational(0), Rational(0), Rational(0)),
                 1 + ListPolynomial(Rational(-2), Rational(0), Rational(0), Rational(0)),
-                "test 5"
+                "test 6"
             )
             assertEquals(
                 ListPolynomial(Rational(-1)),
                 1 + ListPolynomial(Rational(-2)),
-                "test 6"
+                "test 7"
             )
             assertEquals(
                 ListPolynomial(Rational(2)),
                 2 + ListPolynomial(),
-                "test 7"
+                "test 8"
             )
         }
     }
     @Test
     fun test_Int_Polynomial_minus() {
-        RationalField.listPolynomial {
+        RationalField.listPolynomialSpace {
             assertEquals(
                 ListPolynomial(Rational(32, 9), Rational(-8, 9), Rational(-8, 7)),
                 3 - ListPolynomial(Rational(-5, 9), Rational(8, 9), Rational(8, 7)),
@@ -163,31 +197,36 @@ class ListPolynomialTest {
                 -2 - ListPolynomial(Rational(-2)),
                 "test 3"
             )
+            assertEquals(
+                ListPolynomial(Rational(-32, 9), Rational(-8, -9), Rational(8, 7)),
+                0 - ListPolynomial(Rational(32, 9), Rational(-8, 9), Rational(-8, 7)),
+                "test 4"
+            )
             assertEquals(
                 ListPolynomial(),
                 0 - ListPolynomial(),
-                "test 4"
+                "test 5"
             )
             assertEquals(
                 ListPolynomial(Rational(1), Rational(0), Rational(0), Rational(0)),
                 -1 - ListPolynomial(Rational(-2), Rational(0), Rational(0), Rational(0)),
-                "test 5"
+                "test 6"
             )
             assertEquals(
                 ListPolynomial(Rational(1)),
                 -1 - ListPolynomial(Rational(-2)),
-                "test 6"
+                "test 7"
             )
             assertEquals(
                 ListPolynomial(Rational(-2)),
                 -2 - ListPolynomial(),
-                "test 7"
+                "test 8"
             )
         }
     }
     @Test
     fun test_Int_Polynomial_times() {
-        IntModuloRing(35).listPolynomial {
+        IntModuloRing(35).listPolynomialSpace {
             assertEquals(
                 ListPolynomial(34, 2, 1, 20, 2),
                 27 * ListPolynomial(22, 26, 13, 15, 26),
@@ -198,11 +237,22 @@ class ListPolynomialTest {
                 15 * ListPolynomial(7, 0, 49, 21, 14),
                 "test 2"
             )
+            val polynomial = ListPolynomial(22, 26, 13, 15, 26)
+            assertSame(
+                zero,
+                0 * polynomial,
+                "test 3"
+            )
+            assertSame(
+                polynomial,
+                1 * polynomial,
+                "test 4"
+            )
         }
     }
     @Test
     fun test_Polynomial_Constant_plus() {
-        RationalField.listPolynomial {
+        RationalField.listPolynomialSpace {
             assertEquals(
                 ListPolynomial(Rational(-22, 9), Rational(-8, 9), Rational(-8, 7)),
                 ListPolynomial(Rational(5, 9), Rational(-8, 9), Rational(-8, 7)) + Rational(-3),
@@ -242,7 +292,7 @@ class ListPolynomialTest {
     }
     @Test
     fun test_Polynomial_Constant_minus() {
-        RationalField.listPolynomial {
+        RationalField.listPolynomialSpace {
             assertEquals(
                 ListPolynomial(Rational(32, 9), Rational(-8, 9), Rational(-8, 7)),
                 ListPolynomial(Rational(5, 9), Rational(-8, 9), Rational(-8, 7)) - Rational(-3),
@@ -282,7 +332,7 @@ class ListPolynomialTest {
     }
     @Test
     fun test_Polynomial_Constant_times() {
-        IntModuloRing(35).listPolynomial {
+        IntModuloRing(35).listPolynomialSpace {
             assertEquals(
                 ListPolynomial(34, 2, 1, 20, 2),
                 ListPolynomial(22, 26, 13, 15, 26) * 27.asConstant(),
@@ -297,7 +347,7 @@ class ListPolynomialTest {
     }
     @Test
     fun test_Constant_Polynomial_plus() {
-        RationalField.listPolynomial {
+        RationalField.listPolynomialSpace {
             assertEquals(
                 ListPolynomial(Rational(-22, 9), Rational(-8, 9), Rational(-8, 7)),
                 Rational(-3) + ListPolynomial(Rational(5, 9), Rational(-8, 9), Rational(-8, 7)),
@@ -337,7 +387,7 @@ class ListPolynomialTest {
     }
     @Test
     fun test_Constant_Polynomial_minus() {
-        RationalField.listPolynomial {
+        RationalField.listPolynomialSpace {
             assertEquals(
                 ListPolynomial(Rational(32, 9), Rational(-8, 9), Rational(-8, 7)),
                 Rational(3) - ListPolynomial(Rational(-5, 9), Rational(8, 9), Rational(8, 7)),
@@ -377,7 +427,7 @@ class ListPolynomialTest {
     }
     @Test
     fun test_Constant_Polynomial_times() {
-        IntModuloRing(35).listPolynomial {
+        IntModuloRing(35).listPolynomialSpace {
             assertEquals(
                 ListPolynomial(34, 2, 1, 20, 2),
                 27 * ListPolynomial(22, 26, 13, 15, 26),
@@ -392,7 +442,7 @@ class ListPolynomialTest {
     }
     @Test
     fun test_Polynomial_unaryMinus() {
-        RationalField.listPolynomial {
+        RationalField.listPolynomialSpace {
             assertEquals(
                 ListPolynomial(Rational(-5, 9), Rational(8, 9), Rational(8, 7)),
                 -ListPolynomial(Rational(5, 9), Rational(-8, 9), Rational(-8, 7)),
@@ -407,7 +457,7 @@ class ListPolynomialTest {
     }
     @Test
     fun test_Polynomial_Polynomial_plus() {
-        RationalField.listPolynomial {
+        RationalField.listPolynomialSpace {
             // (5/9 - 8/9 x - 8/7 x^2) + (-5/7 + 5/1 x + 5/8 x^2) ?= -10/63 + 37/9 x - 29/56 x^2
             assertEquals(
                 ListPolynomial(Rational(-10, 63), Rational(37, 9), Rational(-29, 56)),
@@ -440,7 +490,7 @@ class ListPolynomialTest {
     }
     @Test
     fun test_Polynomial_Polynomial_minus() {
-        RationalField.listPolynomial {
+        RationalField.listPolynomialSpace {
             // (5/9 - 8/9 x - 8/7 x^2) - (-5/7 + 5/1 x + 5/8 x^2) ?= 80/63 - 53/9 x - 99/56 x^2
             assertEquals(
                 ListPolynomial(Rational(80, 63), Rational(-53, 9), Rational(-99, 56)),
@@ -473,7 +523,7 @@ class ListPolynomialTest {
     }
     @Test
     fun test_Polynomial_Polynomial_times() {
-        IntModuloRing(35).listPolynomial {
+        IntModuloRing(35).listPolynomialSpace {
             // (1 + x + x^2) * (1 - x + x^2) ?= 1 + x^2 + x^4
             assertEquals(
                 ListPolynomial(1, 0, 1, 0, 1),

kmath-functions/src/commonTest/kotlin/space/kscience/kmath/functions/ListPolynomialUtilTest.kt

@@ -5,6 +5,7 @@
 
 package space.kscience.kmath.functions
 
+import space.kscience.kmath.misc.UnstableKMathAPI
 import space.kscience.kmath.test.misc.Rational
 import space.kscience.kmath.test.misc.RationalField
 import kotlin.test.Test
@@ -12,6 +13,7 @@ import kotlin.test.assertEquals
 import kotlin.test.assertFailsWith
 
 
+@OptIn(UnstableKMathAPI::class)
 class ListPolynomialUtilTest {
     @Test
     fun test_substitute_Double() {

kmath-functions/src/commonTest/kotlin/space/kscience/kmath/functions/NumberedConstructorsTest.kt

@@ -0,0 +1,111 @@
+/*
+ * Copyright 2018-2021 KMath contributors.
+ * Use of this source code is governed by the Apache 2.0 license that can be found in the license/LICENSE.txt file.
+ */
+
+package space.kscience.kmath.functions
+
+import space.kscience.kmath.misc.UnstableKMathAPI
+import space.kscience.kmath.operations.algebra
+import space.kscience.kmath.operations.invoke
+import kotlin.test.Test
+import kotlin.test.assertEquals
+
+
+class NumberedConstructorsTest {
+    @Test
+    @UnstableKMathAPI
+    fun testBuilder() {
+        assertEquals(
+            NumberedPolynomialAsIs(
+                listOf(2u, 0u, 3u) to 5,
+                listOf(0u, 1u) to -6,
+            ),
+            Int.algebra.numberedPolynomialSpace {
+                NumberedPolynomial {
+                    5 { 1 inPowerOf 2u; 3 inPowerOf 3u }
+                    (-6) { 2 inPowerOf 1u }
+                }
+            },
+            "test 1"
+        )
+        assertEquals(
+            NumberedPolynomialAsIs(
+                listOf<UInt>() to -1,
+            ),
+            Int.algebra.numberedPolynomialSpace {
+                NumberedPolynomial {
+                    5 { }
+                    (-6) { }
+                }
+            },
+            "test 2"
+        )
+        assertEquals(
+            NumberedPolynomialAsIs(
+                listOf(2u) to -1,
+            ),
+            Int.algebra.numberedPolynomialSpace {
+                NumberedPolynomial {
+                    5 { 1 inPowerOf 1u; 1 inPowerOf 1u }
+                    (-6) { 1 inPowerOf 2u }
+                }
+            },
+            "test 3"
+        )
+    }
+    @Test
+    @UnstableKMathAPI
+    fun testFabric() {
+        assertEquals(
+            NumberedPolynomialAsIs(
+                listOf(2u, 0u, 3u) to 5,
+                listOf(0u, 1u) to -6,
+            ),
+            Int.algebra {
+                NumberedPolynomial(
+                    listOf(2u, 0u, 3u) to 5,
+                    listOf(0u, 1u) to -6,
+                )
+            },
+            "test 1"
+        )
+        assertEquals(
+            NumberedPolynomialAsIs(
+                listOf(2u, 0u, 3u) to 5,
+                listOf(0u, 1u) to -6,
+            ),
+            Int.algebra {
+                NumberedPolynomial(
+                    listOf(2u, 0u, 3u, 0u) to 5,
+                    listOf(0u, 1u, 0u, 0u) to -6,
+                )
+            },
+            "test 2"
+        )
+        assertEquals(
+            NumberedPolynomialAsIs(
+                listOf<UInt>() to -1,
+            ),
+            Int.algebra {
+                NumberedPolynomial(
+                    listOf(0u) to 5,
+                    listOf(0u, 0u) to -6,
+                )
+            },
+            "test 3"
+        )
+        assertEquals(
+            NumberedPolynomialAsIs(
+                listOf<UInt>() to 0,
+            ),
+            Int.algebra {
+                NumberedPolynomial(
+                    listOf(0u) to 5,
+                    listOf(0u, 0u) to -5,
+                )
+            },
+            "test 4"
+        )
+    }
+}

kmath-functions/src/commonTest/kotlin/space/kscience/kmath/functions/NumberedPolynomialUtilTest.kt

@@ -0,0 +1,293 @@
+/*
+ * Copyright 2018-2021 KMath contributors.
+ * Use of this source code is governed by the Apache 2.0 license that can be found in the license/LICENSE.txt file.
+ */
+
+package space.kscience.kmath.functions
+
+import space.kscience.kmath.test.misc.Rational
+import space.kscience.kmath.test.misc.RationalField
+import space.kscience.kmath.test.misc.assertContentEquals
+import kotlin.test.Test
+import kotlin.test.assertEquals
+
+
+class NumberedPolynomialUtilTest {
+    @Test
+    fun test_substitute_Double_Map() {
+        assertContentEquals(
+            mapOf(emptyList<UInt>() to 0.0),
+            NumberedPolynomialAsIs(
+                listOf<UInt>() to 1.0,
+                listOf(1u) to -2.0,
+                listOf(2u) to 1.0,
+            ).substitute(mapOf(
+                0 to 1.0
+            )).coefficients,
+            0.001,
+            "test 1"
+        )
+        assertContentEquals(
+            mapOf(
+                listOf<UInt>() to 0.8597048543814783,
+                listOf(1u) to 0.22997637465889875,
+                listOf(2u) to 0.32675302591924016,
+                listOf(0u, 1u) to 0.4561746111587508,
+                listOf(1u, 1u) to 0.5304946210170756,
+                listOf(2u, 1u) to 0.6244313712888998,
+                listOf(0u, 2u) to 0.2700930201481795,
+                listOf(1u, 2u) to -0.06962351375204712,
+                listOf(2u, 2u) to -0.015206988092131501,
+            ),
+            NumberedPolynomialAsIs(
+                listOf<UInt>() to 0.8597048543814783,
+                listOf(1u) to 0.22997637465889875,
+                listOf(2u) to 0.32675302591924016,
+                listOf(0u, 1u) to 0.4561746111587508,
+                listOf(1u, 1u) to 0.5304946210170756,
+                listOf(2u, 1u) to 0.6244313712888998,
+                listOf(0u, 2u) to 0.2700930201481795,
+                listOf(1u, 2u) to -0.06962351375204712,
+                listOf(2u, 2u) to -0.015206988092131501,
+            ).substitute(mapOf()).coefficients,
+            0.001,
+            "test 2"
+        )
+        assertContentEquals(
+            mapOf(
+                listOf<UInt>() to 0.8597048543814783,
+                listOf(0u, 1u) to 0.4561746111587508,
+                listOf(0u, 2u) to 0.2700930201481795,
+            ),
+            NumberedPolynomialAsIs(
+                listOf<UInt>() to 0.8597048543814783,
+                listOf(1u) to 0.22997637465889875,
+                listOf(2u) to 0.32675302591924016,
+                listOf(0u, 1u) to 0.4561746111587508,
+                listOf(1u, 1u) to 0.5304946210170756,
+                listOf(2u, 1u) to 0.6244313712888998,
+                listOf(0u, 2u) to 0.2700930201481795,
+                listOf(1u, 2u) to -0.06962351375204712,
+                listOf(2u, 2u) to -0.015206988092131501,
+            ).substitute(mapOf(
+                0 to 0.0
+            )).coefficients,
+            0.001,
+            "test 3"
+        )
+        assertContentEquals(
+            mapOf(
+                listOf<UInt>() to 1.433510890645169,
+                listOf(1u) to 0.6264844682514724,
+                listOf(2u) to 0.8405727903771333,
+            ),
+            NumberedPolynomialAsIs(
+                listOf<UInt>() to 0.8597048543814783,
+                listOf(1u) to 0.22997637465889875,
+                listOf(2u) to 0.32675302591924016,
+                listOf(0u, 1u) to 0.4561746111587508,
+                listOf(1u, 1u) to 0.5304946210170756,
+                listOf(2u, 1u) to 0.6244313712888998,
+                listOf(0u, 2u) to 0.2700930201481795,
+                listOf(1u, 2u) to -0.06962351375204712,
+                listOf(2u, 2u) to -0.015206988092131501,
+            ).substitute(mapOf(
+                1 to 0.8400458576651112
+            )).coefficients,
+            0.001,
+            "test 4"
+        )
+        assertContentEquals(
+            mapOf(
+                listOf<UInt>() to 1.934530767358133,
+            ),
+            NumberedPolynomialAsIs(
+                listOf<UInt>() to 0.8597048543814783,
+                listOf(1u) to 0.22997637465889875,
+                listOf(2u) to 0.32675302591924016,
+                listOf(0u, 1u) to 0.4561746111587508,
+                listOf(1u, 1u) to 0.5304946210170756,
+                listOf(2u, 1u) to 0.6244313712888998,
+                listOf(0u, 2u) to 0.2700930201481795,
+                listOf(1u, 2u) to -0.06962351375204712,
+                listOf(2u, 2u) to -0.015206988092131501,
+            ).substitute(mapOf(
+                0 to 0.4846192734143442,
+                1 to 0.8400458576651112,
+            )).coefficients,
+            0.001,
+            "test 5"
+        )
+        assertContentEquals(
+            mapOf(
+                listOf<UInt>() to 0.8597048543814783,
+                listOf(1u) to 0.22997637465889875,
+                listOf(2u) to 0.32675302591924016,
+                listOf(0u, 1u) to 0.4561746111587508,
+                listOf(1u, 1u) to 0.5304946210170756,
+                listOf(2u, 1u) to 0.6244313712888998,
+                listOf(0u, 2u) to 0.2700930201481795,
+                listOf(1u, 2u) to -0.06962351375204712,
+                listOf(2u, 2u) to -0.015206988092131501,
+            ),
+            NumberedPolynomialAsIs(
+                listOf<UInt>() to 0.8597048543814783,
+                listOf(1u) to 0.22997637465889875,
+                listOf(2u) to 0.32675302591924016,
+                listOf(0u, 1u) to 0.4561746111587508,
+                listOf(1u, 1u) to 0.5304946210170756,
+                listOf(2u, 1u) to 0.6244313712888998,
+                listOf(0u, 2u) to 0.2700930201481795,
+                listOf(1u, 2u) to -0.06962351375204712,
+                listOf(2u, 2u) to -0.015206988092131501,
+            ).substitute(mapOf(
+                5 to 0.9211194782050933
+            )).coefficients,
+            0.001,
+            "test 6"
+        )
+    }
+    @Test
+    fun test_substitute_Constant() {
+        assertEquals(
+            NumberedPolynomialAsIs(
+                listOf<UInt>() to Rational(0)
+            ),
+            NumberedPolynomialAsIs(
+                listOf<UInt>() to Rational(1),
+                listOf(1u) to Rational(-2),
+                listOf(2u) to Rational(1)
+            ).substitute(RationalField, mapOf(
+                0 to Rational(1)
+            )),
+            "test 1"
+        )
+        // https://www.wolframalpha.com/input?i=%28-3%2F2+%2B+8%2F6+x+%2B+14%2F6+x%5E2%29+%2B+%28-3%2F1+%2B+-19%2F2+x+%2B+9%2F4+x%5E2%29+y+%2B+%285%2F5+%2B+18%2F9+x+%2B+5%2F2+x%5E2%29+y%5E2+where+x+%3D+-2%2F5%2C+y+%3D+12%2F9
+        assertEquals(
+            NumberedPolynomialAsIs(
+                listOf<UInt>() to Rational(143, 150)
+            ),
+            NumberedPolynomialAsIs(
+                listOf<UInt>() to Rational(-3, 2),
+                listOf(1u) to Rational(8, 6),
+                listOf(2u) to Rational(14, 6),
+                listOf(0u, 1u) to Rational(-3, 1),
+                listOf(1u, 1u) to Rational(-19, 2),
+                listOf(2u, 1u) to Rational(9, 4),
+                listOf(0u, 2u) to Rational(5, 5),
+                listOf(1u, 2u) to Rational(18, 9),
+                listOf(2u, 2u) to Rational(5, 2),
+            ).substitute(RationalField, mapOf(
+                0 to Rational(-2, 5),
+                1 to Rational(12, 9),
+            )),
+            "test 2"
+        )
+        // https://www.wolframalpha.com/input?i=%28%28-3%2F2+%2B+8%2F6+x+%2B+14%2F6+x%5E2%29+%2B+%28-3%2F1+%2B+-19%2F2+x+%2B+9%2F4+x%5E2%29+y+%2B+%285%2F5+%2B+18%2F9+x+%2B+5%2F2+x%5E2%29+y%5E2%29+p%5E8+where+x+%3D+q%2Fp%2C+y+%3D+x%5E3%2C+p+%3D+-2%2F5%2C+q+%3D+12%2F9
+        assertEquals(
+            NumberedPolynomialAsIs(
+            listOf<UInt>() to Rational(47639065216, 2562890625)
+            ),
+            NumberedPolynomialAsIs(
+                listOf(8u) to Rational(-3, 2),
+                listOf(7u, 1u) to Rational(8, 6),
+                listOf(6u, 2u) to Rational(14, 6),
+                listOf(5u, 3u) to Rational(-3, 1),
+                listOf(4u, 4u) to Rational(-19, 2),
+                listOf(3u, 5u) to Rational(9, 4),
+                listOf(2u, 6u) to Rational(5, 5),
+                listOf(1u, 7u) to Rational(18, 9),
+                listOf(0u, 8u) to Rational(5, 2),
+            ).substitute(RationalField, mapOf(
+                0 to Rational(-2, 5),
+                1 to Rational(12, 9),
+            )),
+            "test 3"
+        )
+        // https://www.wolframalpha.com/input?i=%28%28-3%2F2+%2B+8%2F6+x+%2B+14%2F6+x%5E2%29+%2B+%28-3%2F1+%2B+-19%2F2+x+%2B+9%2F4+x%5E2%29+y+%2B+%285%2F5+%2B+18%2F9+x+%2B+5%2F2+x%5E2%29+y%5E2%29+p%5E8+where+x+%3D+q%2Fp%2C+y+%3D+x%5E3%2C+p+%3D+-2%2F5%2C+q+%3D+12%2F9
+        assertEquals(
+            NumberedPolynomialAsIs(
+                listOf(8u) to Rational(-3, 2),
+                listOf(7u, 1u) to Rational(8, 6),
+                listOf(6u, 2u) to Rational(14, 6),
+                listOf(5u, 3u) to Rational(-3, 1),
+                listOf(4u, 4u) to Rational(-19, 2),
+                listOf(3u, 5u) to Rational(9, 4),
+                listOf(2u, 6u) to Rational(5, 5),
+                listOf(1u, 7u) to Rational(18, 9),
+                listOf(0u, 8u) to Rational(5, 2),
+            ),
+            NumberedPolynomialAsIs(
+                listOf(8u) to Rational(-3, 2),
+                listOf(7u, 1u) to Rational(8, 6),
+                listOf(6u, 2u) to Rational(14, 6),
+                listOf(5u, 3u) to Rational(-3, 1),
+                listOf(4u, 4u) to Rational(-19, 2),
+                listOf(3u, 5u) to Rational(9, 4),
+                listOf(2u, 6u) to Rational(5, 5),
+                listOf(1u, 7u) to Rational(18, 9),
+                listOf(0u, 8u) to Rational(5, 2),
+            ).substitute(RationalField, mapOf<Int, Rational>()),
+            "test 4"
+        )
+    }
+    @Test
+    fun test_substitute_Polynomial() {
+        assertEquals(
+            NumberedPolynomialAsIs(
+                listOf<UInt>() to Rational(0)
+            ),
+            NumberedPolynomialAsIs(
+                listOf<UInt>() to Rational(1),
+                listOf(1u) to Rational(-2),
+                listOf(2u) to Rational(1)
+            ).substitute(RationalField, mapOf(
+                0 to NumberedPolynomialAsIs(
+                    listOf<UInt>() to Rational(1)
+                )
+            )),
+            "test 1"
+        )
+        // https://www.wolframalpha.com/input?i=%28-3%2F2+%2B+8%2F6+x+%2B+14%2F6+x%5E2%29+%2B+%28-3%2F1+%2B+-19%2F2+x+%2B+9%2F4+x%5E2%29+y+%2B+%285%2F5+%2B+18%2F9+x+%2B+5%2F2+x%5E2%29+y%5E2+where+x+%3D+-2%2F5%2C+y+%3D+12%2F9
+        assertEquals(
+            NumberedPolynomialAsIs(
+                listOf<UInt>() to Rational(-3, 2),
+                listOf(0u, 1u) to Rational(-92, 21),
+                listOf(0u, 2u) to Rational(-2627, 2352),
+                listOf(0u, 3u) to Rational(4565, 3136),
+                listOf(0u, 4u) to Rational(605, 1568),
+                listOf(1u) to Rational(-20, 3),
+                listOf(1u, 1u) to Rational(1445, 21),
+                listOf(1u, 2u) to Rational(-13145, 392),
+                listOf(1u, 3u) to Rational(-3025, 196),
+                listOf(2u) to Rational(175, 3),
+                listOf(2u, 1u) to Rational(2475, 28),
+                listOf(2u, 2u) to Rational(15125, 98),
+                listOf(3u) to Rational(0),
+                listOf(3u, 1u) to Rational(0),
+                listOf(4u) to Rational(0),
+            ),
+            NumberedPolynomialAsIs(
+                listOf<UInt>() to Rational(-3, 2),
+                listOf(1u) to Rational(8, 6),
+                listOf(2u) to Rational(14, 6),
+                listOf(0u, 1u) to Rational(-3, 1),
+                listOf(1u, 1u) to Rational(-19, 2),
+                listOf(2u, 1u) to Rational(9, 4),
+                listOf(0u, 2u) to Rational(5, 5),
+                listOf(1u, 2u) to Rational(18, 9),
+                listOf(2u, 2u) to Rational(5, 2),
+            ).substitute(RationalField, mapOf(
+                0 to NumberedPolynomialAsIs(
+                    listOf(1u) to Rational(-5, 1),
+                    listOf(0u, 1u) to Rational(2, 8),
+                ),
+                1 to NumberedPolynomialAsIs(
+                    listOf(1u) to Rational(0, 5),
+                    listOf(0u, 1u) to Rational(11, 7),
+                ),
+            )),
+            "test 2"
+        )
+    }
+}

kmath-functions/src/commonTest/kotlin/space/kscience/kmath/test/misc/IntModulo.kt

@@ -0,0 +1,142 @@
+/*
+ * Copyright 2018-2021 KMath contributors.
+ * Use of this source code is governed by the Apache 2.0 license that can be found in the license/LICENSE.txt file.
+ */
+
+package space.kscience.kmath.test.misc
+
+import space.kscience.kmath.functions.ListPolynomial
+import space.kscience.kmath.functions.ListPolynomialSpace
+import space.kscience.kmath.functions.PolynomialSpaceOverRing
+import space.kscience.kmath.operations.Ring
+
+
+class IntModulo {
+    val residue: Int
+    val modulus: Int
+
+    @PublishedApi
+    internal constructor(residue: Int, modulus: Int, toCheckInput: Boolean = true) {
+        if (toCheckInput) {
+            require(modulus != 0) { "modulus can not be zero" }
+            this.modulus = if (modulus < 0) -modulus else modulus
+            this.residue = residue.mod(modulus)
+        } else {
+            this.residue = residue
+            this.modulus = modulus
+        }
+    }
+
+    constructor(residue: Int, modulus: Int) : this(residue, modulus, true)
+
+    operator fun unaryPlus(): IntModulo = this
+    operator fun unaryMinus(): IntModulo =
+        IntModulo(
+            if (residue == 0) 0 else modulus - residue,
+            modulus,
+            toCheckInput = false
+        )
+    operator fun plus(other: IntModulo): IntModulo {
+        require(modulus == other.modulus) { "can not add two residue different modulo" }
+        return IntModulo(
+            (residue + other.residue) % modulus,
+            modulus,
+            toCheckInput = false
+        )
+    }
+    operator fun plus(other: Int): IntModulo =
+        IntModulo(
+            (residue + other) % modulus,
+            modulus,
+            toCheckInput = false
+        )
+    operator fun minus(other: IntModulo): IntModulo {
+        require(modulus == other.modulus) { "can not subtract two residue different modulo" }
+        return IntModulo(
+            (residue - other.residue) % modulus,
+            modulus,
+            toCheckInput = false
+        )
+    }
+    operator fun minus(other: Int): IntModulo =
+        IntModulo(
+            (residue - other) % modulus,
+            modulus,
+            toCheckInput = false
+        )
+    operator fun times(other: IntModulo): IntModulo {
+        require(modulus == other.modulus) { "can not multiply two residue different modulo" }
+        return IntModulo(
+            (residue * other.residue) % modulus,
+            modulus,
+            toCheckInput = false
+        )
+    }
+    operator fun times(other: Int): IntModulo =
+        IntModulo(
+            (residue * other) % modulus,
+            modulus,
+            toCheckInput = false
+        )
+    operator fun div(other: IntModulo): IntModulo {
+        require(modulus == other.modulus) { "can not divide two residue different modulo" }
+        val (reciprocalCandidate, gcdOfOtherResidueAndModulus) = bezoutIdentityWithGCD(other.residue, modulus)
+        require(gcdOfOtherResidueAndModulus == 1) { "can not divide to residue that has non-trivial GCD with modulo" }
+        return IntModulo(
+            (residue * reciprocalCandidate) % modulus,
+            modulus,
+            toCheckInput = false
+        )
+    }
+    operator fun div(other: Int): IntModulo {
+        val (reciprocalCandidate, gcdOfOtherResidueAndModulus) = bezoutIdentityWithGCD(other, modulus)
+        require(gcdOfOtherResidueAndModulus == 1) { "can not divide to residue that has non-trivial GCD with modulo" }
+        return IntModulo(
+            (residue * reciprocalCandidate) % modulus,
+            modulus,
+            toCheckInput = false
+        )
+    }
+    override fun equals(other: Any?): Boolean =
+        when (other) {
+            is IntModulo -> residue == other.residue && modulus == other.modulus
+            else -> false
+        }
+
+    override fun hashCode(): Int = residue.hashCode()
+
+    override fun toString(): String = "$residue mod $modulus"
+}
+
+@Suppress("EXTENSION_SHADOWED_BY_MEMBER", "OVERRIDE_BY_INLINE", "NOTHING_TO_INLINE")
+class IntModuloRing : Ring<IntModulo> {
+
+    val modulus: Int
+
+    constructor(modulus: Int) {
+        require(modulus != 0) { "modulus can not be zero" }
+        this.modulus = if (modulus < 0) -modulus else modulus
+    }
+
+    override inline val zero: IntModulo get() = IntModulo(0, modulus, toCheckInput = false)
+    override inline val one: IntModulo get() = IntModulo(1, modulus, toCheckInput = false)
+
+    fun number(arg: Int) = IntModulo(arg, modulus, toCheckInput = false)
+
+    override inline fun add(left: IntModulo, right: IntModulo): IntModulo = left + right
+    override inline fun multiply(left: IntModulo, right: IntModulo): IntModulo = left * right
+
+    override inline fun IntModulo.unaryMinus(): IntModulo = -this
+    override inline fun IntModulo.plus(arg: IntModulo): IntModulo = this + arg
+    override inline fun IntModulo.minus(arg: IntModulo): IntModulo = this - arg
+    override inline fun IntModulo.times(arg: IntModulo): IntModulo = this * arg
+    inline fun IntModulo.div(arg: IntModulo): IntModulo = this / arg
+}
+
+fun ListPolynomialSpace<IntModulo, IntModuloRing>.ListPolynomial(vararg coefs: Int): ListPolynomial<IntModulo> =
+    ListPolynomial(coefs.map { IntModulo(it, ring.modulus) })
+fun IntModuloRing.ListPolynomial(vararg coefs: Int): ListPolynomial<IntModulo> =
+    ListPolynomial(coefs.map { IntModulo(it, modulus) })
+
+fun IntModuloRing.m(arg: Int) = IntModulo(arg, modulus)
+fun PolynomialSpaceOverRing<IntModulo, *, IntModuloRing>.m(arg: Int) = IntModulo(arg, ring.modulus)

kmath-functions/src/commonTest/kotlin/space/kscience/kmath/test/misc/Rational.kt

@@ -0,0 +1,135 @@
+/*
+ * Copyright 2018-2021 KMath contributors.
+ * Use of this source code is governed by the Apache 2.0 license that can be found in the license/LICENSE.txt file.
+ */
+
+package space.kscience.kmath.test.misc
+
+import space.kscience.kmath.misc.UnstableKMathAPI
+import space.kscience.kmath.operations.Field
+import space.kscience.kmath.operations.NumbersAddOps
+
+class Rational {
+    companion object {
+        val ZERO: Rational = Rational(0L)
+        val ONE: Rational = Rational(1L)
+    }
+
+    val numerator: Long
+    val denominator: Long
+
+    internal constructor(numerator: Long, denominator: Long, toCheckInput: Boolean = true) {
+        if (toCheckInput) {
+            if (denominator == 0L) throw ArithmeticException("/ by zero")
+
+            val greatestCommonDivider = gcd(numerator, denominator).let { if (denominator < 0L) -it else it }
+
+            this.numerator = numerator / greatestCommonDivider
+            this.denominator = denominator / greatestCommonDivider
+        } else {
+            this.numerator = numerator
+            this.denominator = denominator
+        }
+    }
+
+    constructor(numerator: Int, denominator: Int) : this(numerator.toLong(), denominator.toLong(), true)
+    constructor(numerator: Int, denominator: Long) : this(numerator.toLong(), denominator, true)
+    constructor(numerator: Long, denominator: Int) : this(numerator, denominator.toLong(), true)
+    constructor(numerator: Long, denominator: Long) : this(numerator, denominator, true)
+    constructor(numerator: Int) : this(numerator.toLong(), 1L, false)
+    constructor(numerator: Long) : this(numerator, 1L, false)
+
+    operator fun unaryPlus(): Rational = this
+    operator fun unaryMinus(): Rational = Rational(-this.numerator, this.denominator)
+    operator fun plus(other: Rational): Rational =
+        Rational(
+            numerator * other.denominator + denominator * other.numerator,
+            denominator * other.denominator
+        )
+    operator fun plus(other: Int): Rational =
+        Rational(
+            numerator + denominator * other.toLong(),
+            denominator
+        )
+    operator fun plus(other: Long): Rational =
+        Rational(
+            numerator + denominator * other,
+            denominator
+        )
+    operator fun minus(other: Rational): Rational =
+        Rational(
+            numerator * other.denominator - denominator * other.numerator,
+            denominator * other.denominator
+        )
+    operator fun minus(other: Int): Rational =
+        Rational(
+            numerator - denominator * other.toLong(),
+            denominator
+        )
+    operator fun minus(other: Long): Rational =
+        Rational(
+            numerator - denominator * other,
+            denominator
+        )
+    operator fun times(other: Rational): Rational =
+        Rational(
+            numerator * other.numerator,
+            denominator * other.denominator
+        )
+    operator fun times(other: Int): Rational =
+        Rational(
+            numerator * other.toLong(),
+            denominator
+        )
+    operator fun times(other: Long): Rational =
+        Rational(
+            numerator * other,
+            denominator
+        )
+    operator fun div(other: Rational): Rational =
+        Rational(
+            numerator * other.denominator,
+            denominator * other.numerator
+        )
+    operator fun div(other: Int): Rational =
+        Rational(
+            numerator,
+            denominator * other.toLong()
+        )
+    operator fun div(other: Long): Rational =
+        Rational(
+            numerator,
+            denominator * other
+        )
+    override fun equals(other: Any?): Boolean =
+        when (other) {
+            is Rational -> numerator == other.numerator && denominator == other.denominator
+            is Int -> numerator == other && denominator == 1L
+            is Long -> numerator == other && denominator == 1L
+            else -> false
+        }
+
+    override fun hashCode(): Int = 31 * numerator.hashCode() + denominator.hashCode()
+
+    override fun toString(): String = if (denominator == 1L) "$numerator" else "$numerator/$denominator"
+}
+
+@Suppress("EXTENSION_SHADOWED_BY_MEMBER", "OVERRIDE_BY_INLINE", "NOTHING_TO_INLINE")
+@OptIn(UnstableKMathAPI::class)
+object RationalField : Field<Rational>, NumbersAddOps<Rational> {
+    override inline val zero: Rational get() = Rational.ZERO
+    override inline val one: Rational get() = Rational.ONE
+
+    override inline fun number(value: Number): Rational = Rational(value.toLong())
+
+    override inline fun add(left: Rational, right: Rational): Rational = left + right
+    override inline fun multiply(left: Rational, right: Rational): Rational = left * right
+    override inline fun divide(left: Rational, right: Rational): Rational = left / right
+    override inline fun scale(a: Rational, value: Double): Rational = a * number(value)
+
+    override inline fun Rational.unaryMinus(): Rational = -this
+    override inline fun Rational.plus(arg: Rational): Rational = this + arg
+    override inline fun Rational.minus(arg: Rational): Rational = this - arg
+    override inline fun Rational.times(arg: Rational): Rational = this * arg
+    override inline fun Rational.div(arg: Rational): Rational = this / arg
+}

kmath-functions/src/commonTest/kotlin/space/kscience/kmath/test/misc/assertion.kt

@@ -0,0 +1,14 @@
+/*
+ * Copyright 2018-2021 KMath contributors.
+ * Use of this source code is governed by the Apache 2.0 license that can be found in the license/LICENSE.txt file.
+ */
+
+package space.kscience.kmath.test.misc
+
+import kotlin.test.assertEquals
+
+
+fun <T> assertContentEquals(expected: Map<T, Double>, actual: Map<T, Double>, absoluteTolerance: Double, message: String? = null) {
+    assertEquals(expected.keys, actual.keys, message)
+    for ((key, expectedValue) in expected) assertEquals(expectedValue, actual[key]!!, absoluteTolerance, message)
+}

kmath-functions/src/commonTest/kotlin/space/kscience/kmath/test/misc/misc.kt

@@ -0,0 +1,29 @@
+/*
+ * Copyright 2018-2021 KMath contributors.
+ * Use of this source code is governed by the Apache 2.0 license that can be found in the license/LICENSE.txt file.
+ */
+
+package space.kscience.kmath.test.misc
+
+import kotlin.math.abs
+
+
+data class BezoutIdentityWithGCD<T>(val first: T, val second: T, val gcd: T)
+
+tailrec fun gcd(a: Long, b: Long): Long = if (a == 0L) abs(b) else gcd(b % a, a)
+
+fun bezoutIdentityWithGCD(a: Int, b: Int): BezoutIdentityWithGCD<Int> =
+    when {
+        a < 0 && b < 0 -> with(bezoutIdentityWithGCDInternalLogic(-a, -b, 1, 0, 0, 1)) { BezoutIdentityWithGCD(-first, -second, gcd) }
+        a < 0 -> with(bezoutIdentityWithGCDInternalLogic(-a, b, 1, 0, 0, 1)) { BezoutIdentityWithGCD(-first, second, gcd) }
+        b < 0 -> with(bezoutIdentityWithGCDInternalLogic(a, -b, 1, 0, 0, 1)) { BezoutIdentityWithGCD(first, -second, gcd) }
+        else -> bezoutIdentityWithGCDInternalLogic(a, b, 1, 0, 0, 1)
+    }
+
+internal tailrec fun bezoutIdentityWithGCDInternalLogic(a: Int, b: Int, m1: Int, m2: Int, m3: Int, m4: Int): BezoutIdentityWithGCD<Int> =
+    if (b == 0) BezoutIdentityWithGCD(m1, m3, a)
+    else {
+        val quotient = a / b
+        val reminder = a % b
+        bezoutIdentityWithGCDInternalLogic(b, reminder, m2, m1 - quotient * m2, m4, m3 - quotient * m4)
+    }